Algebraic theory of block codes detecting independent errors
type: Item
instance of: scholarly article
title: Algebraic theory of block codes detecting independent errors
zbMATH Open document ID: 0418.94011
DOI: 10.1007/BF01084252
published in: Journal of Soviet Mathematics
publication date: 1976-01-01T00:00:00Z
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 94-02
Mathematics Subject Classification ID: 94Bxx
zbMATH DE Number: 3652245
zbMATH Keywords: survey of algebraic coding theory
zbMATH Keywords: block codes
zbMATH Keywords: bounds of cardinality
zbMATH Keywords: perfect and uniformly packed codes
zbMATH Keywords: constraints of weight spectra
zbMATH Keywords: cyclic codes
zbMATH Keywords: Bch codes
zbMATH Keywords: Goppa codes
zbMATH Keywords: Abelian group codes
zbMATH Keywords: Reed-Muller codes
zbMATH Keywords: polynomial codes
zbMATH Keywords: concatenated codes
zbMATH Keywords: bibliography
author: Victor A. Zinoviev
MaRDI profile type: Publication
cites work: Q5519684
cites work: Q5675263
cites work: Q4079493
cites work: A necessary condition for the existence of perfect codes in Lie metric
cites work: On the theory of group codes
cites work: Semisimple cyclic and Abelian codes. II
cites work: Q4068585
cites work: Q4068584
cites work: Q3250141
cites work: Q5635524
cites work: Q5620525
cites work: Q5601776
cites work: Q4044441
cites work: Q5675260
cites work: Q4068578
cites work: Q5540093
cites work: Q5671906
cites work: Q4048937
cites work: Q5678751
cites work: Q4085606
cites work: Q4105590
cites work: A note on the decomposition of cyclic codes into cyclic classes
cites work: A New Class of Cyclic Codes
cites work: Perfect codes and the Mathieu groups
cites work: On tactical configurations and error-correcting codes
cites work: New 5-designs
cites work: On weights in quadratic-residue codes
cites work: Contractions of self-orthogonal codes
cites work: Coding and Combinatorics
cites work: Weights of irreducible cyclic codes
cites work: Some additional upper bounds for fixed-weight codes of specified minimum distance
cites work: The Enumeration of Information Symbols in BCH Codes
cites work: Algebraic coding theory
cites work: Factoring Polynomials Over Large Finite Fields
cites work: The weight enumerators for certain subcodes of the second order binary Reed-Muller codes
cites work: Some Mathematical Properties of a Scheme for Reducing the Bandwidth of Motion Pictures by Hadamard Smearing
cites work: Coding theory and the Mathieu groups
cites work: Long primitive binary BCH codes have distance&lt;tex&gt;d leq 2n ln R^{-1}/log n cdots&lt;/tex&gt;
cites work: Goppa codes
cites work: Some long cyclic linear binary codes are not so bad
cites work: Q5672672
cites work: Gleason's theorem on self-dual codes
cites work: Extended double-error-correcting binary Goppa codes are cyclic (Corresp.)
cites work: On the solution of algebraic equations over finite fields
cites work: Restrictions on weight distribution of Reed-Muller codes
cites work: Weight enumerator for second-order Reed-Muller codes
cites work: Weight distributions of the cosets of the (32,6) Reed-Muller code
cites work: Q3285034
cites work: Orthogonal Arrays of Strength two and three
cites work: On a class of error correcting binary group codes
cites work: Further results on error correcting binary group codes
cites work: A note on a result in the theory of code construction
cites work: Some Factorizations of 2 n ± 1 and Related Results
cites work: On primitive trinomials (Mod 2)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Polynômes des poids de certains codes et fonctions thêta de certains réseaux

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Cyclic product codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Orthogonal Arrays of Index Unity

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On a class of wide-sense binary BCH codes whose minimum distances exceed the BCH bound (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On majority-logic decoding of finite geometry codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Note on majority-logic decoding of finite geometry codes (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Some results on quasi-cyclic codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Further results on polynomial codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A geometric approach to a class of cyclic codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: BCH Bounds for a Class of Cyclic Codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On cyclic codes that are invariant under the general linear group

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Reachable sets for linear dynamical systems

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Q4119093

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Weights of linear codes and strongly regular normed spaces

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Four fundamental parameters of a code and their combinatorial significance

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Q5707657

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Q4055513

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Q5613703

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Unrestricted codes with the Golay parameters are unique

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On generalized ReedMuller codes and their relatives

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A self-dual even (96, 48, 16) code (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Upper bounds for fixed-weight codes of specified minimum distance (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Q5538637

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Analysis of weight distribution in binary cyclic codes (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Factorization of cyclic codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Cyclic error-locating codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On the Golay perfect binary code

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On a class of majority-logic decodable cyclic codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Nearly perfect binary codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Augmentation techniques for a class of product codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Rook domains, Latin squares, affine planes, and error-distributing codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Two-error correcting Bose-Chaudhuri codes are quasi-perfect

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A Class of Error-Correcting Codes in $p^m $ Symbols

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On the Number of Information Symbols in Difference-Set Cyclic Codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Q4766989

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On the p-rank of the incidence matrix of a balanced or partially balanced incomplete block design and its applications to error correcting codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A note on the minimum distance structure of cyclic codes (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Decoding beyond the BCH bound (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Q4404128

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On the structure of generalized finite-geometry codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A bound for cyclic codes of composite length (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Generalizations of the BCH bound

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On some classes of cyclic codes of composite length (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Decoding beyond the BCH bound using multiple sets of syndrome sequences (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Some results on the minimum distance structure of cyclic codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Srivastava codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Noncyclic generalizations of BCH and srivastava codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Minimum-distance bounds for binary linear codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Shortened BCH codes (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Q3265111

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Circulant bases for cyclic codes (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Improved asymptotic bounds for error-correcting codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On upper bounds for unrestricted binary-error-correcting codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Upper bounds for constant weight error correcting codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Class of constructive asymptotically good algebraic codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: New binary coding results by circulants

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On Finding Low Weight Vectors in Quadratic Residue Codes for $p = 8m - 1$

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Some lower bounds on the minimum weight of cyclic codes of composite length

Algebraic theory of block codes detecting independent errors (cites work)
cites work: An upper bound on&lt;tex&gt;k/n&lt;/tex&gt;for affine-invariant codes with fixed&lt;tex&gt;d/n&lt;/tex&gt;(Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: The weight enumerators for several classes of subcodes of the 2nd order binary Reed-Muller codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A Gilbert-Varshamov bound for quasi-cycle codes of rate 1/2 (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Construction and decomposition of cyclic codes of composite length (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On majority-logic decoding for duals of primitive polynomial codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Some results on the minimum weight of primitive BCH codes (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Some results on cyclic codes which are invariant under the affine group and their applications

Algebraic theory of block codes detecting independent errors (cites work)
cites work: New generalizations of the Reed-Muller codes--I: Primitive codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Polynomial codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Some Remarks on BCH Bounds and Minimum Weights of Binary Primitive BCH Codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On the weight structure of Reed-Muller codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On the weight enumeration of weights less than 2.5d of Reed—Muller codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A class of low-rate nonlinear binary codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A new theorem about the Mattson-Solomon polynomial, and some applications

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Quasi-self-reciprocal polynomials and potentially large minimum distance BCH codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Coset analysis of reed muller codes via translates of finite vector spaces

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Some Sphere Packings in Higher Space

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Notes on Sphere Packings

Algebraic theory of block codes detecting independent errors (cites work)
cites work: New sphere packings in dimensions 9-15

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Sphere Packings and Error-Correcting Codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Analysis and synthesis of polynomials and sequences over&lt;tex&gt;GF(2)&lt;/tex&gt;

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Two theorems on perfect codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Shortened finite geometry codes (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Number of information symbols in polynomial codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Multifold Euclidean geometry codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Long BCH codes are bad

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Further results on cyclic product codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On Group and Nongroup Perfect Codes in $q$ Symbols.

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On the nonexistence of perfect 2- and 3-hamming-error-correcting codes over GF(q)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Q5655266

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Coding theory

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A new description of the Nadler code (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Q4053464

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A theorem on equidistant codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A construction scheme for linear and non-linear codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On the Minimum Distance of Bose-Chaudhuri-Hocquenghem Codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: The Structure and Properties of Binary Cyclic Alphabets

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Q4055514

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Binary Codes Which Are Ideals in the Group Algebra of an Abelian Group

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On Binary Cyclic Codes Which are Also Cyclic Codes Over $GF(2^s )$

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Cyclotomic numbers, coding theory and orthogonal polynomials

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Orthogonal circulant matrices over finite fields, and how to find them

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Generalizations of Gleason's theorem on weight enumerators of self-dual codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On the p-rank of the design matrix of a difference set

Algebraic theory of block codes detecting independent errors (cites work)
cites work: The MacWilliams Identities for Nonlinear Codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Good self dual codes exist

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On the existence of a projective plane of order 10

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Design Methods for Maximum Minimum-Distance Error-Correcting Codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Q3213326

Algebraic theory of block codes detecting independent errors (cites work)
cites work: An upper bound for self-dual codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Weight enumerators of self-orthogonal codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A vector-space packing problem

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On the number of information symbols in Bose-Chaudhuri codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Graph theoretic error-correcting codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Reversible codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On the fractional weight of distinct binary&lt;tex&gt;n&lt;/tex&gt;-tuples (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Polynomial weights and code constructions

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A New Treatment of Bose-Chaudhuri Codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On the symmetry of good nonlinear codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On periodic sequences from \(GF(q)\)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Euler products, cyclotomy, and coding

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A 32-point n=12, d=5 code (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A note on cyclic permutation error-correcting codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: An optimum nonlinear code

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Q5181218

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Maximal Group Codes with Specified Minimum Distance

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Q3290963

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Q5665102

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Limit distribution of the minimum distance of random linear codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Power moment identities on weight distributions in error correcting codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On the uniqueness of the Golay codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On a new family of symmetry codes and related new five-designs

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A classification of self-orthogonal codes over GF(2)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Symmetry codes over GF(3) and new five-designs

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Self-dual codes over gf(q) satisfy a modified varshamov-gilbert bound

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Binary self-dual codes of length 24

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Weight and distance structure of Nordstrom-Robinson quadratic code

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A class of optimum nonlinear double-error-correcting codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A new look at the Golay (23, 12) code (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A (48, 31, 8) linear code (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Polynomial Codes Over Certain Finite Fields

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A class of majority logic decodable codes (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On linear and nonlinear single-error-correcting q-nary perfect codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On the weight distribution of cyclic codes (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Q3845688

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Codes with simple automorphism groups

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A Metrization for Power-Sets with Applications to Combinatorial Analysis

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Maximum distance&lt;tex&gt;q&lt;/tex&gt;-nary codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Sphere packings constructed from BCH and Justesen codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A survey of constructive coding theory, and a table of binary codes of highest known rate

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Is there a (72,36) d = 16 self-dual code? (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Q4053457

Algebraic theory of block codes detecting independent errors (cites work)
cites work: New binary codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A NEW FAMILY OF NONLINEAR CODES OBTAINED FROM CONFERENCE MATRICES

Algebraic theory of block codes detecting independent errors (cites work)
cites work: New family of single-error correcting codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On the p-rank of the incidence matrix of points and hyperplanes in a finite projective geometry

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A weight formula for group codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Weights of cyclic codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Algebraically punctured cyclic codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A modification of the constructive asymptotically good codes of Justesen for low rates

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Factorization of polynomials over finite fields

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On the decomposition of cyclic codes into cyclic classes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Q5609848

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On the Nonexistence of Perfect Codes over Finite Fields

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Q4041437

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Self-orthogonal quasi-cyclic codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A search technique for quasi-perfect codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: A low-rate improvement on the Elias bound (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: New generalizations of the Reed-Muller codes--II: Nonprimitive codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Justesen's construction--The low-rate case (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On codes derivable from the tensor product of check matrices

Algebraic theory of block codes detecting independent errors (cites work)
cites work: On an extended class of error-locating codes

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Adding Two Information Symbols to Certain Nonbinary BCH Codes and Some Applications

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Nonbinary random error-correcting codes (Corresp.)

Algebraic theory of block codes detecting independent errors (cites work)
cites work: Linear Recurring Sequences

Algebraic theory of block codes detecting independent errors (full work available at URL)
full work available at URL: https://doi.org/10.1007/bf01084252

Algebraic theory of block codes detecting independent errors (OpenAlex ID)
OpenAlex ID: W2051067291