Recent progress on weight distributions of cyclic codes over finite fields

DOI10.13069/jacodesmath.36866zbMath1371.94683OpenAlexW2338778237MaRDI QIDQ307903

Chengju Li, Qin Yue, Hai Quang Dinh

Publication date: 5 September 2016

Published in: Journal of Algebra, Combinatorics, Discrete Structures and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.13069/jacodesmath.36866

zbMATH Keywords

exponential sumsfinite fieldsGauss sumsGauss periodslinear codesquadratic formsweight distributioncyclic codes

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Other character sums and Gauss sums (11T24) Cyclic codes (94B15)

Related Items (20)

A transform approach to polycyclic and serial codes over rings ⋮ On the weight distributions of some cyclic codes ⋮ A survey on the applications of Niho exponents ⋮ The weight distributions of irreducible cyclic codes of length 2npm ⋮ Unnamed Item ⋮ Octanary linear codes using simplicial complexes ⋮ Weight enumerators of some irreducible cyclic codes of odd length ⋮ The weight distribution of irreducible cyclic codes associated with decomposable generalized Paley graphs ⋮ Weight enumerators of reducible cyclic codes and their dual codes ⋮ Weight distribution of cyclic codes defined by quadratic forms and related curves ⋮ A class of three-weight linear codes and their complete weight enumerators ⋮ Hamming weight enumerators of multi-twisted codes with at most two non-zero constituents ⋮ Complete weight enumerators of a family of three-weight linear codes ⋮ Complete classification of \((\delta +\alpha u^2)\)-constacyclic codes over \(\mathbb {F}_{3^m}[u/\langle u^4\rangle \) of length \(3n\)] ⋮ The Weight Distribution for an Extended Family of Reducible Cyclic Codes ⋮ The subfield codes of several classes of linear codes ⋮ A class of subfield codes of linear codes and their duals ⋮ Complete weight enumerators of a class of two-weight linear codes ⋮ Complete weight enumerators of a class of linear codes with two or three weights ⋮ A class of constacyclic codes containing formally self-dual and isodual codes

Cites Work

• Unnamed Item
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• A Mathematical Theory of Communication
• Weight distributions of cyclic codes with respect to pairwise coprime order elements
• The weight distributions of some cyclic codes with three or four nonzeros over \(\mathbb F_3\)
• Repeated-root constacyclic codes of length \(\ell p^s\) and their duals
• A class of six-weight cyclic codes and their weight distribution
• Constacyclic codes of length \(p^s\) over \(\mathbb F_{p^m} + u\mathbb F_{p^m}\)
• The weight distribution of a class of \(p\)-ary cyclic codes
• Complete solving of explicit evaluation of Gauss sums in the index 2 case
• Repeated-root constacyclic codes of length
• On cyclic codes of length \(2^{2^r}-1\) with two zeros whose dual codes have three weights
• Planar functions and planes of Lenz-Barlotti class II
• Constacyclic codes over finite fields
• Cyclic codes with few weights and Niho exponents
• The weight distributions of a class of cyclic codes
• The weight distributions of two classes of \(p\)-ary cyclic codes
• Two-weight cyclic codes constructed as the direct sum of two one-weight cyclic codes
• On Niho type cross-correlation functions of \(m\)-sequences
• The weight distributions of cyclic codes with two zeros and zeta functions
• Three addition theorems for some q-Krawtchouk polynomials
• Some results about the cross-correlation function between two maximal linear sequences
• Codes, bent functions and permutations suitable for DES-like cryptosystems
• On three weights in cyclic codes with two zeros.
• All two-weight irreducible cyclic codes?
• Highly nonlinear mappings
• Hamming weights in irreducible cyclic codes
• The weight distributions of a class of cyclic codes. III
• Structure of repeated-root constacyclic codes of length \(3p^s\) and their duals
• The weight distributions of a class of cyclic codes. II
• New classes of 2-weight cyclic codes
• Projective two-weight irreducible cyclic and constacyclic codes
• Weight distribution of some reducible cyclic codes
• A class of three-weight cyclic codes
• On self-dual cyclic codes over finite chain rings
• Kloosterman sum identities and low-weight codewords in a cyclic code with two zeros
• On the linear ordering of some classes of negacyclic and cyclic codes and their distance distributions
• Error-correcting linear codes. Classification by isometry and applications. With CD-ROM
• Weight distributions of a class of cyclic codes from \(\mathbb F_l\)-conjugates
• Planes of order \(n\) with collineation groups of order \(n^ 2\)
• The Weight Distributions of Several Classes of Cyclic Codes From APN Monomials
• Hamming Weights of the Duals of Cyclic Codes With Two Zeros
• On the Weight Distribution of Cyclic Codes With Niho Exponents
• Some New Results on the Cross Correlation of <inline-formula> <tex-math notation="TeX">$m$ </tex-math></inline-formula>-Sequences
• The Weight Distribution of a Class of Cyclic Codes Related to Hermitian Forms Graphs
• The Weight Distributions of Cyclic Codes and Elliptic Curves
• Cyclic and Negacyclic Codes Over Finite Chain Rings
• Are&lt;tex&gt;$2$&lt;/tex&gt;-Weight Projective Cyclic Codes Irreducible?
• The weight distribution of a class of linear codes from perfect nonlinear functions
• Value Distributions of Exponential Sums From Perfect Nonlinear Functions and Their Applications
• On the Weight Distributions of Two Classes of Cyclic Codes
• Cyclic Codes and Sequences From Generalized Coulter–Matthews Function
• The Geometry of Two-Weight Codes
• On cyclic MDS codes of length q over GF(q) (Corresp.)
• On subfield subcodes of modified Reed-Solomon codes (Corresp.)
• Some two-weight codes with composite parity-check polynomials (Corresp.)
• Period polynomials and Gauss sums for finite fields
• Semisimple cyclic and Abelian codes. II
• Negacyclic and cyclic codes over Z/sub 4/
• Constacyclic codes, cocycles and a u+v|u-v construction
• Families of curves and weight distributions of codes
• Weight Divisibility of Cyclic Codes, Highly Nonlinear Functions on F2m, and Crosscorrelation of Maximum-Length Sequences
• The Weight Distribution of Some Irreducible Cyclic Codes
• The Weight Distribution of an Extended Class of Reducible Cyclic Codes
• The Weight Distributions of the Duals of Cyclic Codes With Two Zeros
• The Weight Enumerator of a Class of Cyclic Codes
• Cyclic Codes and Sequences: The Generalized Kasami Case
• Weight Distributions of Two Classes of Cyclic Codes With Respect to Two Distinct Order Elements
• Five Families of Three-Weight Ternary Cyclic Codes and Their Duals
• A Family of Five-Weight Cyclic Codes and Their Weight Enumerators
• Evaluation of the Weight Distribution of a Class of Cyclic Codes Based on Index 2 Gauss Sums
• Weight Distribution of a Class of Cyclic Codes With Arbitrary Number of Zeros
• A General Description for the Weight Distribution of Some Reducible Cyclic Codes
• The Weight Enumerator of Three Families of Cyclic Codes
• On the Walsh Transform of a Class of Functions From Niho Exponents
• Power moment identities on weight distributions in error correcting codes
• The weight enumerators for several classes of subcodes of the 2nd order binary Reed-Muller codes
• Polynomial weights and code constructions
• On repeated-root cyclic codes
• Repeated-root cyclic codes
• A note on the cross-correlation function between two binary maximal length linear sequences
• The structure of 1-generator quasi-twisted codes and new linear codes

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