Shift-register synthesis and BCH decoding

From MaRDI portal
Publication:5554046

DOI10.1109/TIT.1969.1054260zbMath0167.18101OpenAlexW2162442687WikidataQ56081990 ScholiaQ56081990MaRDI QIDQ5554046

James L. Massey

Publication date: 1969

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1109/tit.1969.1054260



Related Items

On linear complexity of sequences over \(\text{GF}(2^n)\), A look-ahead algorithm for the solution of general Hankel systems, Matrix-product structure of repeated-root cyclic codes over finite fields, The Gauss quadrature for general linear functionals, Lanczos algorithm, and minimal partial realization, Polynomial-division-based algorithms for computing linear recurrence relations, Trace representation and linear complexity of binary sequences derived from Fermat quotients, On evaluating the linear complexity of a sequence of least period \(2^ n\), Early termination in sparse interpolation algorithms, On finite length nonbinary sequences with large nonlinear complexity over the residue ring \(\mathbb{Z}_m\), Polynomial-exponential decomposition from moments, Linear complexity profiles and jump complexity, Determining the \(k\)-error joint linear complexity spectrum for a binary multisequence with period \(p^n\), Perfect factors in the de Bruijn graph, The Berlekamp-Massey algorithm and linear recurring sequences over a factorial domain, On the \(\mathrm{GF}(p)\) linear complexity of Hall's sextic sequences and some cyclotomic-set-based sequences, On the \(k\)-error linear complexity over \({\mathbb F}_p\) of Legendre and Sidelnikov sequences, Finding a minimal set of linear recurring relations capable of generating a given finite two-dimensional array, An extension of binary threshold sequences from Fermat quotients, Modelling the shrinking generator in terms of linear CA, Linear recurring sequences over modules, The complexity of a periodic sequence over GF(p), Simple algorithms for decoding systematic Reed-Solomon codes, Linear recurring sequences over rings and modules, New inversion formulas for matrices classified in terms of their distance from Toeplitz matrices, Algebraic attacks on a class of stream ciphers with unknown output function, The linear complexity of a class of binary sequences with optimal autocorrelation, Characterising the linear complexity of span 1 de Bruijn sequences over finite fields., A modified Guruswami-Sudan algorithm for decoding Reed-Solomon codes, Orthogonal sequences of polynomials over arbitrary fields, On the linear complexity of binary lattices, Distribution of one-error linear complexity of binary sequences for arbitrary prime period, An algorithm for constructing a minimal partial realization in the multivariable case, The set of reversible \(90/150\) cellular automata is regular, Generation of full cycles by a composition of NLFSRs, Quadratic functions with prescribed spectra, Trace representation of pseudorandom binary sequences derived from Euler quotients, Construction of balanced Boolean functions with high nonlinearity and good autocorrelation properties, On the Berlekamp/Massey algorithm and counting singular Hankel matrices over a finite field, Extended Games-Chan algorithm for the 2-adic complexity of FCSR-sequences., On lattice-based algebraic feedback shift registers synthesis for multisequences, The exact autocorrelation distribution and 2-adic complexity of a class of binary sequences with almost optimal autocorrelation, On the linear complexity and the autocorrelation of generalized cyclotomic binary sequences of length \(2p^m\), Characteristic digit-sum sequences, Linear complexity of binary sequences derived from Euler quotients with prime-power modulus, On Dillon's class \(H\) of bent functions, Niho bent functions and o-polynomials, A study of MBH-type realization algorithms, On the security of the Feng-Liao-Yang Boolean functions with optimal algebraic immunity against fast algebraic attacks, New classes of quaternary cyclotomic sequence of length \(2p^m\) with high linear complexity, The transformation between the Galois NLFSRs and the Fibonacci NLFSRs via semi-tensor product of matrices, New techniques for the computation of linear recurrence coefficients, A lattice-based minimal partial realization algorithm for matrix sequences of varying length, Two-dimensional shift register synthesis and Gröbner bases for polynomial ideals over an integer residue ring, A lower bound on the 2-adic complexity of the modified Jacobi sequence, Enhanced Boolean functions suitable for the filter model of pseudo-random generator, On sequences, rational functions and decomposition, Solving the FCSR synthesis problem for multi-sequences by lattice basis reduction, The Lanczos algorithm and Hankel matrix factorization, AFSRs synthesis with the extended Euclidean rational approximation algorithm, On finite pseudorandom binary lattices, Expansion complexity and linear complexity of sequences over finite fields, An iterative algorithm for parametrization of shortest length linear shift registers over finite chain rings, Perfect staircase profile of linear complexity for finite sequences, Inversion components of block Hankel-like matrices, On minimal polynomials over \(\mathbb F_{q^m}\) and over \(\mathbb F_q\) of a finite-length sequence over \(\mathbb F_{q^m}\), On the structure of order domains, Analysis of the generalized self-shrinking generator, A wide family of nonlinear filter functions with a large linear span, On the joint linear complexity profile of explicit inversive multisequences, Extension of the Berlekamp-Massey algorithm to N dimensions, On the linear complexities of two classes of quaternary sequences of even length with optimal autocorrelation, Automatic complexity of shift register sequences, Bounded distance decoding of linear error-correcting codes with Gröbner bases, Reducing the calculation of the linear complexity of \(u_2^v\)-periodic binary sequences to Games-Chan algorithm, Cryptology: The mathematics of secure communication, Linear complexity and correlation of a class of binary cyclotomic sequences, On Elkies subgroups of \(\ell\)-torsion points in elliptic curves defined over a finite field, Recursive partial realization from the combined sequence of Markov parameters and moments, A linear algebraic approach to multisequence shift-register synthesis, A canonical matrix continued fraction solution of the minimal (partial) realization problem, Factorization of determinants over finite fields and application in stream ciphers, A simple Hankel interpretation of the Berlekamp-Massey algorithm, A rank theorem for Vandermonde matrices, New upper bounds on the linear complexity, On the linear complexity profile of some new explicit inversive pseudorandom numbers, Characterization of \(2^{n}\)-periodic binary sequences with fixed 2-error or 3-error linear complexity, A type of recurring relation on sequences and efficient decoding of a class of algebraic-geometric codes. I, Gröbner bases of characteristic ideals of LRS over UFD, On the complexities of de-Bruijn sequences, Challenges of symbolic computation: My favorite open problems. With an additional open problem by Robert M. Corless and David J. Jeffrey, A new efficient algorithm for computing Gröbner bases \((F_4)\), On the partial realization problem, On the linear complexity profile of explicit nonlinear pseudorandom numbers., Finding recursions for multidimensional arrays, Cross-correlations of geometric sequences in characteristic two, Estimation of arithmetic means and their applications in guessing theory, Displacement structure for Hankel, Vandermonde, and related (derived) matrices, Complexity analysis of binary nonlinear feedforward sequences through minimum polynomials of compound matrices, Recursive partial realization for 2-D data arrays, Counting functions and expected values for the \(k\)-error linear complexity, The vulnerability of geometric sequences based on fields of odd characteristic, State-Space Realizations of Periodic Convolutional Codes, On the k-error linear complexity of binary sequences derived from polynomial quotients, Linear complexity of second order PN_sequences addition with single order PN_sequence in nonlinear filter generator, ON DECODING ALGORITHMS FOR GENERALIZED REED — SOLOMON CODES WITH ERRORS AND ERASURES. II, ON THE BERLEKAMP — MASSEY ALGORITHM AND ITS APPLICATION FOR DECODING ALGORITHMS, Periods Distribution in the Linear Feedback Generalized Registers, A method for analyzing repetitive pseudorandom sequences by the criterion of Markov chain entropy, On the linear complexity and autocorrelation of generalized cyclotomic binary sequences with period \(4p^n \), Analysis and computation of multidimensional linear complexity of periodic arrays, Key-recovery fault injection attack on the classic McEliece KEM, An extension of binary cyclotomic sequences having order 2lt, Interpolation of dense and sparse rational functions and other improvements in \texttt{FireFly}, The weight recursions for the 2-rotation symmetric quartic Boolean functions, An extension of a construction of covering arrays, Computing the periods of preimages in surjective cellular automata, A LINEAR COMPLEXITY ANALYSIS OF QUADRATIC RESIDUES AND PRIMITIVE ROOTS SPACINGS, Research problems, Modified Berlekamp-Massey Algorithm for Approximating the k-Error Linear Complexity of Binary Sequences, Randomness and Representation of Span n Sequences, 2-Adic and Linear Complexities of a Class of Whiteman’s Generalized Cyclotomic Sequences of Order Four, A relationship between the Berlekamp-Massey and the euclidean algorithms for linear feedback shift register synthesis, Some Enumeration Results on Binary 2n-Periodic Sequences, Randomness measures related to subset occurrence, Linear Complexity of Binary Threshold Sequences Derived from Generalized Polynomial Quotient with Prime-Power Modulus, Transform decoding of BCH codes overZm, The irreducibility of some level 1 Hecke polynomials, Rational complexity of binary sequences, F\(\mathbb{Q}\)SRs, and pseudo-ultrametric continued fractions in \(\mathbb{R}\), Jump and hop randomness tests for binary sequences, A New Algorithm for Decoding Reed-Solomon Codes, Linear algebra for computing Gröbner bases of linear recursive multidimensional sequences, PERIODS ON TWO KINDS OF NONLINEAR FEEDBACK SHIFT REGISTERS WITH TIME VARYING FEEDBACK FUNCTIONS, On Fast and Provably Secure Message Authentication Based on Universal Hashing, On the evaluation codes given by simple \(\delta \)-sequences, Fast Correlation Attacks over Extension Fields, Large-Unit Linear Approximation and Cryptanalysis of SNOW 2.0, On the linear complexity of product sequences of linear recurring sequences, Computing the reciprocal of units in Galois rings, An L-Banded Approximation to the Inverse of Symmetric Toeplitz Matrices, Studies on the distribution of the shortest linear recurring sequences, A lookup table decoding of systematic \((47, 24, 11)\) quadratic residue code, Construction and decoding of BCH codes over chain of commutative rings, On ideal \(t\)-tuple distribution of orthogonal functions in filtering de Bruijn generators, Linear complexity over \(\mathbb{F}_q\) and 2-adic complexity of a class of binary generalized cyclotomic sequences with good autocorrelation, On the annihilator ideal of an inverse form, A Lower Bound on the Expected Complexity in the Set of n-Tuples of Given Weight, Arrays composed from the extended rational cycle, Recovering highly-complex linear recurrences of integer sequences, Cryptographic pseudo-random sequences from the chaotic Hénon map, Discrete linear models for the generalized self-shrunken sequences, Linear complexity of a new class of quaternary generalized cyclotomic sequence with period \(2 p^m\), A Decoding Approach to Reed–Solomon Codes from Their Definition, Efficient information-theoretic secure multiparty computation over \(\mathbb{Z}/p^k\mathbb{Z}\) via Galois rings, Refined convergents to the associated continued fractions for binary sequences, A family of weightwise (almost) perfectly balanced Boolean functions with optimal algebraic immunity, Structure analysis on the \(k\)-error linear complexity for \(2^n\)-periodic binary sequences, A new construction of rotation symmetric Boolean functions with optimal algebraic immunity and higher nonlinearity, Open Questions on Nonlinearity and on APN Functions, In-depth comparison of the Berlekamp-Massey-Sakata and the Scalar-FGLM algorithms: the adaptive variants, A fast algorithm to compute irreducible and primitive polynomials in finite fields, Shrinking generators based on \(\sigma \)-LFSRs, A fraction free matrix Berlekamp/Massey algorithm, Mixer–a new stream cipher, Linear Span analysis of a set of periodic sequence generators, Some decoding applications of minimal realization, Computation of low-weight parity checks for correlation attacks on stream ciphers, Evaluation codes defined by finite families of plane valuations at infinity, Fast skew-feedback shift-register synthesis, Some new classes of quaternary sequences with low autocorrelation property via two binary cyclotomic sequences, An improved method for predicting truncated multiple recursive generators with unknown parameters, Growth Functions and Automatic Groups, Decoding interleaved Reed-Solomon codes beyond their joint error-correcting capability, On the linear span of the \(p\)-ary cascaded GMW sequences, Threshold data structures and coding theory, TWOPRIME: A fast stream ciphering algorithm, On the linear complexity of generalized cyclotomic sequences with the period \(p^m\), Fast Correlation Attacks: Methods and Countermeasures, Berlekamp-Massey algorithm, continued fractions, Padé approximations, and orthogonal polynomials, A fast parallel sparse polynomial GCD algorithm, Cryptographic properties of some binary generalized cyclotomic sequences with the length \(p^{2}\), Inverse scattering and minimal partial realizations, Stream Ciphering Techniques Based on n-Tuples Juxtaposition Sequences, Sparse polynomial interpolation: sparse recovery, super-resolution, or Prony?, A further study of the linear complexity of new binary cyclotomic sequence of length \(p^r\), Linear feedback shift registers and the minimal realization problem, Minimal realization of linear systems, Subquadratic-time factoring of polynomials over finite fields, Concatenating indicators of flats for designing cryptographic functions, A fuzzy vault scheme, Optimal parameters for the WG stream cipher family, Multi-continued fraction algorithm and generalized B--M algorithm over \(\mathbb F_{q}\), The black-box Niederreiter algorithm and its implementation over the binary field, Binary Pseudo-Random Sequences Theory, Improved Bounds on the Linear Complexity of Keystreams Obtained by Filter Generators, Generalized Joint Linear Complexity of Linear Recurring Multisequences, A Lattice-Based Minimal Partial Realization Algorithm, Parallel Generation of ℓ-Sequences, The Berlekamp-Massey algorithm revisited, Continued fraction for formal Laurent series and the lattice structure of sequences, On the annihilator ideal of an inverse form: addendum, Improving the lower bound on the maximum nonlinearity of 1-resilient Boolean functions and designing functions satisfying all cryptographic criteria, A survey on nonlinear Boolean functions with optimal algebraic immunity suitable for stream ciphers, On algebraic properties of S-boxes designed by means of disjoint linear codes, Construction of Boolean functions with excellent cryptographic criteria using bivariate polynomial representation, Computing isogenies between elliptic curves over $F_{p^n}$ using Couveignes's algorithm, Linear complexity of generalized sequences by comparison of PN-sequences, Fast lattice reduction for $\mathbf {F}_{2}$-linear pseudorandom number generators, A new algorithm on the minimal rational fraction representation of feedback with carry shift registers, Multidimensional linear complexity analysis of periodic arrays, Weights for short quartic Boolean functions, Cryptanalysis of the GPRS encryption algorithms GEA-1 and GEA-2, Compact Normal Form for Regular Languages as Xor Automata, On the constructions of resilient Boolean functions with five-valued Walsh spectra and resilient semi-bent functions, Guessing Gröbner bases of structured ideals of relations of sequences, Investigating the discrepancy property of de Bruijn sequences, A note on good permutation codes from Reed-Solomon codes, Binomial representation of cryptographic binary sequences and its relation to cellular automata, Linear complexity of Ding-Helleseth generalized cyclotomic sequences of order eight, On the stability of periodic binary sequences with zone restriction, Counting functions and expected values for the lattice profile at \(n\), On a family of pseudorandom binary sequences, An efficient binary sequence generator with cryptographic applications, Families of \(p\)-ary sequences with low correlation and large linear complexity, The RCH method for computing minimal polynomials of polynomial matrices, Algebraic attacks on grain-like keystream generators, Additive character sums of polynomial quotients, A realization approach to stochastic model reduction