A family of diameter perfect constant-weight codes from Steiner systems Full article
| Journal |
Journal of Combinatorial Theory. Series A
ISSN: 0097-3165 , E-ISSN: 1096-0899 |
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| Output data | Year: 2023, Volume: 200, Article number : 105790, Pages count : 20 DOI: 10.1016/j.jcta.2023.105790 | ||||||
| Tags | diameter perfect codes, anticodes, constant-weight codes, code--anticode bound, Steiner systems | ||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0017 |
Abstract:
If S is a transitive metric space, then |C|\cdot|A| \le |S| for any distance-$d code C and a set A, ``anticode'', of diameter less than d. For every Steiner S(t,k,n) system S, we show the existence of a q-ary constant-weight code C of length~n, weight~k (or n-k), and distance d=2k-t+1 (respectively, d=n-t+1) and an anticode A of diameter d-1 such that the pair (C,A) attains the code--anticode bound and the supports of the codewords of C are the blocks of S (respectively, the complements of the blocks of S). We study the problem of estimating the minimum value of q for which such a code exists, and find that minimum for small values of t.
Cite:
Shi M.
, Xia Y.
, Krotov D.S.
A family of diameter perfect constant-weight codes from Steiner systems
Journal of Combinatorial Theory. Series A. 2023. V.200. 105790 :1-20. DOI: 10.1016/j.jcta.2023.105790 WOS Scopus РИНЦ OpenAlex
A family of diameter perfect constant-weight codes from Steiner systems
Journal of Combinatorial Theory. Series A. 2023. V.200. 105790 :1-20. DOI: 10.1016/j.jcta.2023.105790 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Dec 9, 2022 |
| Accepted: | Jun 28, 2023 |
| Published print: | Jul 31, 2023 |
| Published online: | Jul 31, 2023 |
Identifiers:
| Web of science: | WOS:001155116300001 |
| Scopus: | 2-s2.0-85169559729 |
| Elibrary: | 62914496 |
| OpenAlex: | W4385438484 |