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New MDS or Near-MDS self-dual codes

Title
New MDS or Near-MDS self-dual codes
Authors
Gulliver T.A.Kim J.-L.Lee Y.
Ewha Authors
이윤진
SCOPUS Author ID
이윤진scopus
Issue Date
2008
Journal Title
IEEE Transactions on Information Theory
ISSN
0018-9448JCR Link
Citation
vol. 54, no. 9, pp. 4354 - 4360
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
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 = 2m (m ≥ 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 ≤ 113. We also construct many new MDS self-dual codes over GF(p) of length 16 for primes 29 ≤ p ≤ 113. Finally, we construct Euclidean/Hermitian self-dual MDS codes of lengths up to 14 over GF(q2) where q = 19, 23, 25, 27, 29. © 2008 IEEE.
DOI
10.1109/TIT.2008.928297
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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