On the classification of perfect codes: Extended side class structures

Heden, OlofKTH,Matematik (Avd.),Department of Mathematics, KTH, Stockholm, Sweden (författare)

On the classification of perfect codes : Extended side class structures

QC 20100525
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.

Hessler, MartinLinköpings universitet,Tillämpad matematik,Tekniska högskolan(Swepub:liu)marhe54 (författare)
Westerbäck, ThomasKTH,Matematik (Avd.),Department of Mathematics, KTH, Stockholm, Sweden(Swepub:kth)u19e52s2 (författare)
KTHMatematik (Avd.) (creator_code:org_t)

Ingår i:Discrete MathematicsAmsterdam, Netherlands : Elsevier310:1, s. 43-550012-365X1872-681X

Av författaren/redakt...: Heden, Olof; Hessler, Martin; Westerbäck, Thom ...

Om ämnet

Kungliga biblioteket hanterar dina personuppgifter i enlighet med EU:s dataskyddsförordning (2018), GDPR. Läs mer om hur det funkar här.
Så här hanterar KB dina uppgifter vid användning av denna tjänst.