Long nonbinary codes exceeding the Gilbert-Varshamov bound for any fixed distance

Authors:
S. Yekhanin;I. Dumer
Affiliations:
Dept. of Electr. Eng. & Comput. Sci., Massachusetts Inst. of Technol., Cambridge, MA, USA;-
Venue:
IEEE Transactions on Information Theory
Year:
2006

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Abstract

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≥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.