Title :
Long nonbinary codes exceeding the Gilbert-Varshamov bound for any fixed distance
Author :
Yekhanin, Sergey ; Dumer, Ilya
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., Massachusetts Inst. of Technol., Cambridge, MA, USA
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.
Keywords :
BCH codes; algebraic codes; linear codes; redundancy; BCH; Bezout theorem; Bose-Chaudhuri-Hocquenghem code; Gilbert-Varshamov bound; algebraic code; minimum asymptotic redundancy; nonbinary code; q-ary code length; Galois fields; Geometry; Lead; Linear code; Parity check codes; Taxonomy; Upper bound; Affine lines; BCH; Bezout's theorem; Bose–Chaudhuri–Hocquenghem; code; norm;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2004.834744
