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| Content Provider | Springer Nature Link |
|---|---|
| Author | Heden, Olof Hessler, Martin |
| Copyright Year | 2006 |
| Abstract | The side class structure of a perfect 1-error correcting binary code (hereafter referred to as a perfect code) C describes the linear relations between the coset representatives of the kernel of C. Two perfect codes C and C′ are linearly equivalent if there exists a non-singular matrix A such that AC = C′ where C and C′ are matrices with the code words of C and C′ as columns. Hessler proved that the perfect codes C and C′ are linearly equivalent if and only if they have isomorphic side class structures. The aim of this paper is to describe all side class structures. It is shown that the transpose of any side class structure is the dual of a subspace of the kernel of some perfect code and vice versa; any dual of a subspace of a kernel of some perfect code is the transpose of the side class structure of some perfect code. The conclusion is that for classification purposes of perfect codes it is sufficient to find the family of all kernels of perfect codes. |
| Ending Page | 333 |
| Page Count | 15 |
| Starting Page | 319 |
| File Format | |
| ISSN | 09251022 |
| e-ISSN | 15737586 |
| Journal | Designs, Codes and Cryptography |
| Issue Number | 3 |
| Volume Number | 40 |
| Language | English |
| Publisher | Kluwer Academic Publishers |
| Publisher Date | 2006-01-01 |
| Publisher Place | Boston |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Information and Communication, Circuits Data Structures, Cryptology and Information Theory Tilings Discrete Mathematics in Computer Science Data Encryption Combinatorial codes Coding and Information Theory Combinatorics Perfect codes |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Discrete Mathematics and Combinatorics Theoretical Computer Science Computer Science Applications |
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