Results 281 to 290 of about 103,237 (307)
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Optimal binary linear codes and Z/sub 4/-linearity
IEEE Transactions on Information Theory, 1996We give necessary and sufficient conditions for a binary linear code to be Z/sub 4/-linear. Especially we treat optimal, binary linear codes and determine all such codes with minimum weight less or equal to six which are Z/sub 4/-linear.
Sylvia B. Encheva, Helge Elbrønd Jensen
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On the Hasse diagram of binary linear codes
Discrete Mathematics, Algorithms and ApplicationsA binary [Formula: see text]-linear code [Formula: see text] is a [Formula: see text]-dimensional subspace of [Formula: see text]. For [Formula: see text], the set [Formula: see text] is a coset of [Formula: see text]. In this work, we study a partial ordering on the set of cosets of a binary linear code [Formula: see text] of length [Formula: see ...
Lisbeth Danyeli Delgado Ordoñez +2 more
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Error-correction capability of binary linear codes
IEEE International Symposium on Information Theory, 2003. Proceedings., 2003The monotone structure of correctable and uncorrectable errors given by the complete decoding for a binary linear code is investigated. New bounds on the error-correction capability of linear codes beyond half the minimum distance are presented, both for the best codes and for arbitrary codes under some restrictions on their parameters.
Tor Helleseth +2 more
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On binary linear [160,80,24] codes
IEEE International Symposium on Information Theory, 2003. Proceedings., 2003This paper discusses the construction of binary linear Golay [160, 80] (mn,mk) codes from an extended Reed Solomon [32, 16] (n, k) code over F/sub 32/ (F/sub 2//sup m/) by concatenating the given code with a suitable basis symmetric representation of Frobenius automorphism F/sub 32/ over F/sub 2/ with a minimum distance 24.
M. van Dijk +3 more
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Proceedings of the Institution of Electrical Engineers, 1974
A class of algebraic linear codes is introduced in which the parity-check matrix of the code is constructed by using a subset of the Abelian group of Walsh functions. These codes meet the Helgert and Stinaff upper bounds on minimum Hamming distance, and all the codes of this class are easily decodable by a one-step majority-logic algorithm.
A.A. Hashim, A.G. Constantinides
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A class of algebraic linear codes is introduced in which the parity-check matrix of the code is constructed by using a subset of the Abelian group of Walsh functions. These codes meet the Helgert and Stinaff upper bounds on minimum Hamming distance, and all the codes of this class are easily decodable by a one-step majority-logic algorithm.
A.A. Hashim, A.G. Constantinides
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On binary linear codes supporting t-designs
IEEE Transactions on Information Theory, 2001The vectors of a given weight support a \(t\)-design if, using the coordinates as points and the vectors as blocks, a \(t\)-design is formed. In this work the author shows that the only self-orthogonal codes, that is those codes \(C\) with \(C \subseteq C^\perp\), with minimum distance less than or equal to \(18\), whose minimum weight vectors hold a \(
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Varieties of binary linear codes
Algebra Universalis, 1999The main objective of the paper is to look at (a part of) the problem of coding from the point of view of universal algebras. To this end, the notion of a binary code conceived as an algebra is introduced. Natural properties of codes are then expressed in universal algebraic language.
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No Projective 16-Divisible Binary Linear Code of Length 131 Exists
IEEE Communications Letters, 2021Sascha Kurz
exaly
A Z/sub 8/-linear lift of the binary Golay code and a nonlinear binary (96,2/sup 37/,24)-code
IEEE Transactions on Information Theory, 2001M Greferath
exaly