New MDS or Near-MDS Self-Dual Codes
New MDS or Near-MDS Self-Dual Codes
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DOI：
10.1109/tit.2008.928297
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发表时间：
2008-09
影响因子：
2.5
通讯作者：
T. Gulliver;Jon-Lark Kim;Yoonjin Lee
中科院分区：
文献类型：
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作者：
T. Gulliver;Jon-Lark Kim;Yoonjin Lee
在大有限域上构造了新的MDS或近MDS自对偶码。特别是，我们发现，存在一个欧几里德自对偶MDS码的长度n = q GF（q），当q = 2 m（m ges 2）使用里德所罗门（RS）码及其扩展。事实证明，这种多描述源（MDS）自对偶码是一种扩展的duadic码。当q = 1（mod 4）且q ≤ 113时，我们从RS码构造了GF（q）上长度为n = q-1的欧几里德自对偶近MDS码.我们还构造了GF（p）上长度为16的素数为29 les ples 113的MDS自对偶码。最后，我们构造了GF（q2）上长度为14的Euclidean/Hermitian自对偶MDS码，其中q = 19，23，25，27，29.
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 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(q2) where q = 19, 23,25, 27, 29.