On the classification of perfect codes: Extended side class structures

On the classification of perfect codes : Extended side class structures

Heden, Olof (author): KTH,Matematik (Avd.),Department of Mathematics, KTH, Stockholm, Sweden

Hessler, Martin (author): Linköpings universitet,Tillämpad matematik,Tekniska högskolan

Westerbäck, Thomas (author): KTH,Matematik (Avd.),Department of Mathematics, KTH, Stockholm, Sweden

KTH Matematik (Avd) (creator_code:org_t)

Amsterdam, Netherlands : Elsevier, 2010
2010
English.
In: Discrete Mathematics. - Amsterdam, Netherlands : Elsevier. - 0012-365X .- 1872-681X. ; 310:1, s. 43-55

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Abstract Subject headings

The two 1-error correcting perfect binary codes, C and C′ are said to be equivalent if there exists a permutation π of the set of the n coordinate positions and a word such that . Hessler defined C and C′ to be linearly equivalent if there exists a non-singular linear map φ such that C′=φ(C). Two perfect codes C and C′ of length n will be defined to be extended equivalent if there exists a non-singular linear map φ and a word such thatHeden and Hessler, associated with each linear equivalence class an invariant LC and this invariant was shown to be a subspace of the kernel of some perfect code. It is shown here that, in the case of extended equivalence, the corresponding invariant will be the extension of the code LC.This fact will be used to give, in some particular cases, a complete enumeration of all extended equivalence classes of perfect codes.

About the subject

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