On the non-existence of extended 1-perfect codes and MDS codes Full article
| Journal |
Journal of Combinatorial Theory. Series A
ISSN: 0097-3165 , E-ISSN: 1096-0899 |
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| Output data | Year: 2022, Volume: 189, Article number : 105607, Pages count : DOI: 10.1016/j.jcta.2022.105607 | ||
| Tags | Completely regular code; Equitable partition; Extended perfect code; Hamming graph; MDS code; Perfect coloring | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Russian Science Foundation | 18-11-00136 |
Abstract:
We prove the non-existence of extended perfect codes in H(n,q), where q=3,4 and n>q+2 or both n and q are odd. In particular, we prove the non-existence of non-linear (q+2,qq−1,4)q MDS codes when q is odd.
Cite:
Bespalov E.
On the non-existence of extended 1-perfect codes and MDS codes
Journal of Combinatorial Theory. Series A. 2022. V.189. 105607 . DOI: 10.1016/j.jcta.2022.105607 WOS Scopus РИНЦ OpenAlex
On the non-existence of extended 1-perfect codes and MDS codes
Journal of Combinatorial Theory. Series A. 2022. V.189. 105607 . DOI: 10.1016/j.jcta.2022.105607 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jan 14, 2022 |
| Accepted: | Feb 9, 2022 |
| Published online: | Feb 24, 2022 |
Identifiers:
| Web of science: | WOS:000793602100003 |
| Scopus: | 2-s2.0-85125122163 |
| Elibrary: | 48184065 |
| OpenAlex: | W4214487603 |