On decomposability of 4-ary distance 2 MDS codes, double-codes, and n-quasigroups of order 4 Full article
| Journal |
Discrete Mathematics
ISSN: 0012-365X , E-ISSN: 1872-681X |
||
|---|---|---|---|
| Output data | Year: 2008, Volume: 308, Number: 15, Pages: 3322-3334 Pages count : 13 DOI: 10.1016/j.disc.2007.06.038 | ||
| Tags | MDS codes, n-ary quasigroups, Decomposability, Reducibility, Frequency hypercubes, Latin hypercubes | ||
| Authors |
|
||
| Affiliations |
|
Abstract:
A subset S of {0, 1, ..., 2t-1}^n is called a t-fold MDS code if every line in each of n base directions contains exactly t elements of S. The adjacency graph of a t-fold MDS code is not connected if and only if the characteristic function of the code is the repetition-free sum of the characteristic functions of t-fold MDS codes of smaller lengths.
In the case t = 2, the theory has the following application. The union of two disjoint (n, 4^{n-1}), 2) MDS codes in {0, 1, 2, 3}^n is a double-MDS-code. If the adjacency graph of the double-MDS-code is not connected, then the double-code can be decomposed into double-MDS-codes of smaller lengths. If the graph has more than two connected components, then the MDS codes are also decomposable. The result has an interpretation as a test for reducibility of n-quasigroups of order 4. (C) 2007 Elsevier B.V. All rights reserved.
Cite:
Krotov D.S.
On decomposability of 4-ary distance 2 MDS codes, double-codes, and n-quasigroups of order 4
Discrete Mathematics. 2008. V.308. N15. P.3322-3334. DOI: 10.1016/j.disc.2007.06.038 WOS Scopus РИНЦ OpenAlex
On decomposability of 4-ary distance 2 MDS codes, double-codes, and n-quasigroups of order 4
Discrete Mathematics. 2008. V.308. N15. P.3322-3334. DOI: 10.1016/j.disc.2007.06.038 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Nov 4, 2005 |
| Accepted: | Jun 22, 2007 |
| Published online: | Aug 7, 2007 |
Identifiers:
| Web of science: | WOS:000257016500021 |
| Scopus: | 2-s2.0-43249091346 |
| Elibrary: | 13579015 |
| OpenAlex: | W2022291866 |