Back to Search
Start Over
NMDS codes of maximal length over [F.sub.q], 8 [less than or equal to] q [less than or equal to] 11
- Source :
- IEEE Transactions on Information Theory. April, 2002, Vol. 48 Issue 4, p963, 4 p.
- Publication Year :
- 2002
-
Abstract
- A linear [[n, k, d].sub.q] code C is called near maximum-distance separable (NMDS) if d(C) = n - k and d([C.sup.[perpendicular to]]) = k. The maximum length of an NMDS [[n, k, d].sup.q] code is denoted by m'(k, q). In this correspondence, it has been verified by a computer-based proof that m'(5, 8) = 15, m'(4, 9) = 16, m'(5, 9) = 16, and 20 [less than or equal to] m'(4, 11) [less than or equal to] 21. Moreover, the NMDS codes of length m'(4.8), m'(5, 8), and m'(4, 9) have been classified. As the dual code of an NMDS code is NMDS, the values of m'(k, 8), k = 10, 11, 12, and of m'(k, 9),k = 12, 13, 14 have been also deduced. Index Terms--Galois fields, linear codes, near maximum-distance separable (NMDS) codes.
- Subjects :
- Codes -- Analysis
Information theory -- Research
Subjects
Details
- ISSN :
- 00189448
- Volume :
- 48
- Issue :
- 4
- Database :
- Gale General OneFile
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- edsgcl.84866867