Long nonbinary codes exceeding the Gilbert-Varshamov bound for any fixed distance
Long nonbinary codes exceeding the Gilbert-Varshamov bound for any fixed distance
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DOI：
10.1109/tit.2004.834744
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发表时间：
2004-06
影响因子：
2.5
通讯作者：
S. Yekhanin;I. Dumer
中科院分区：
文献类型：
--
作者：
S. Yekhanin;I. Dumer
设A（q，n，d）表示长度为n、距离为d的q元码的最大长度。我们研究的最小渐近冗余n增长，而q和d是固定的。对于任何d和q/spl ges/d-1，长代数码的设计，提高了Bose-Chaudhuri-Hocquenghem（BCH）码，并具有最低的渐近冗余已知的日期。在此之前的工作，代码的固定距离，渐近超过BCH码和Gilbert-Varshamov界设计的距离仅为4，5和6。
Let A(q,n,d) denote the maximum size of a q-ary code of length n and distance d. We study the minimum asymptotic redundancy as n grows while q and d are fixed. For any d and q/spl ges/d-1, long algebraic codes are designed that improve on the Bose-Chaudhuri-Hocquenghem (BCH) codes and have the lowest asymptotic redundancy known to date. Prior to this work, codes of fixed distance that asymptotically surpass BCH codes and the Gilbert-Varshamov bound were designed only for distances 4,5, and 6.