On the classification of MDS codes Full article
| Journal |
IEEE Transactions on Information Theory
ISSN: 0018-9448 , E-ISSN: 1557-9654 |
||||||
|---|---|---|---|---|---|---|---|
| Output data | Year: 2015, Volume: 61, Number: 12, Pages: 6485-6492 Pages count : 8 DOI: 10.1109/tit.2015.2488659 | ||||||
| Tags | Code equivalence, error correction codes, Latin hypercubes, MDS codes, perfect codes | ||||||
| Authors |
|
||||||
| Affiliations |
|
Abstract:
A q-ary code of length n, size M, and minimum distanced is called an (n,M,d)q code. An (n,q^k,n-k+1)q code is called a maximum distance separable (MDS) code. In this paper, some MDS codes over small alphabets are classified. It is shown that every (k+d-1,q^k,d)q code with k≥3, d≥3, q∈{5,7} is equivalent to a linear code with the same parameters. This implies that the (6,5^4,3)5 code and the (n,7^{n-2},3)7 MDS codes for n∈{6,7,8} are unique. The classification of one-error-correcting 8-ary MDS codes is also finished; there are 14, 8, 4, and 4 equivalence classes of (n,8^{n-2},3)8 codes for n = 6, 7, 8, and 9, respectively. One of the equivalence classes of perfect (9,8^7,3)8 codes corresponds to the Hamming code and the other three are nonlinear codes for which there exists no previously known construction.
Cite:
Kokkala J.I.
, Krotov D.S.
, Östergård P.R.J.
On the classification of MDS codes
IEEE Transactions on Information Theory. 2015. V.61. N12. P.6485-6492. DOI: 10.1109/tit.2015.2488659 WOS Scopus РИНЦ OpenAlex
On the classification of MDS codes
IEEE Transactions on Information Theory. 2015. V.61. N12. P.6485-6492. DOI: 10.1109/tit.2015.2488659 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Nov 21, 2014 |
| Accepted: | Sep 20, 2015 |
| Published online: | Oct 8, 2015 |
Identifiers:
| Web of science: | WOS:000368420200006 |
| Scopus: | 2-s2.0-84951178439 |
| Elibrary: | 26805798 |
| OpenAlex: | W3100027604 |