Concepedia

The average binary weight-enumerator for a class of generalized Reed-Solomon codes

IEEE Transactions on Information Theory · 1991 · 43 citations · 7 references

Concepts

Explicit Weight-enumeratorCombinatorics On WordEngineeringGeneralized Reed-solomon CodesAlgebraic MethodComputational ComplexityComputer ScienceAverage Binary Weight-enumeratorDiscrete MathematicsBinary ExpansionsCoding TheoryBinary CodesError Correction CodeVariable-length CodeAlgebraic Coding Theory

Abstract

An explicit weight-enumerator for the set of binary expansions of a class of generalized Reed-Solomon codes is derived. This enumerator is then used to show that most of these binary codes are asymptotically good, and to bound the rates of self-intersecting codes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>

References

7

A Theorem on the Distribution of Weights in a Systematic Code†

Jessie MacWilliams · Bell System Technical Journal · 1963 · 413 citations

Systematic Code, Systematic Code†, Engineering +13

On subfield subcodes of modified Reed-Solomon codes (Corresp.)

P. Delsarte · IEEE Transactions on Information Theory · 1975 · 269 citations

Engineering, Subfield Subcodes, Coding Theory +8

On generator matrices of MDS codes (Corresp.)

Ron M. Roth, G. Seroussi · IEEE Transactions on Information Theory · 1985 · 115 citations

Engineering, Coding Theory, Computer Algebra +10

Linear intersecting codes

Gérard Cohen, A. Lempel · Discrete Mathematics · 1985 · 55 citations

Mathematical Programming, Engineering, Linear Intersecting Codes +4

The binary weight distribution of the extended (2m,2m − 4) code of the Reed-Solomon code over GF(2m) with generator polynomial (x − α)(x − α2)(x − α3)

Tadao Kasami, Shu Lin · Linear Algebra and its Applications · 1988 · 41 citations

Generator Polynomial, Binary Weight Distribution, Reed-solomon Code +3