New MDS or Near-MDS Self-Dual Codes

We construct new MDS or near-MDS self-dual codes over large finite fields. In particular, we show that there exists a Euclidean self-dual MDS code of length n = q over GF(q) whenever q = 2 m (m ges 2) using a Reed-Solomon (RS) code and its extension. It turns out that this multiple description sourc...

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Bibliographic Details
Published in:IEEE transactions on information theory 2008-09, Vol.54 (9), p.4354-4360
Main Authors: Gulliver, T.A., Jon-Lark Kim, Yoonjin Lee
Format: Article
Language:English
Subjects:
Applied sciences
Codes
Coding, codes
Construction
Euclidean space
Exact sciences and technology
Galois fields
Information theory
Information, signal and communications theory
Mathematical analysis
Mathematics
Multiple description source (MDS) codes
Reed-Solomon (RS) codes
self-dual codes
Signal and communications theory
Telecommunications and information theory
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Summary:We construct new MDS or near-MDS self-dual codes over large finite fields. In particular, we show that there exists a Euclidean self-dual MDS code of length n = q over GF(q) whenever q = 2 m (m ges 2) using a Reed-Solomon (RS) code and its extension. It turns out that this multiple description source (MDS) self-dual code is an extended duadic code. We construct Euclidean self-dual near-MDS codes of length n = q-1 over GF(q) from RS codes when q = 1 (mod 4) and q les 113. We also construct many new MDS self-dual codes over GF(p) of length 16 for primes 29 les p les 113. Finally, we construct Euclidean/Hermitian self-dual MDS codes of lengths up to 14 over GF(q 2 ) where q = 19, 23,25, 27, 29.
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2008.928297