New DbEC-TbED codes better than the Gilbert-Varshamov bound

Conference Paper · February 2000with1 Read
DOI: 10.1109/ISIT.2000.866322 · Source: IEEE Xplore
Conference: Information Theory, 2000. Proceedings. IEEE International Symposium on
Abstract

A new class of double byte error correcting-triple byte error detecting (DbEC-TbED) codes over GF(q) is constructed. For the cases of q=3,4, the new codes are better than the Gilbert-Varshamov bound

    • "Moreover there are some sporadic cases in the literature for which better results than the ones of [20] exist. The results in these sporadic cases are obtained in [3,5,6,8,10]. They are also summarized in [20]. "
    [Show abstract] [Hide abstract] ABSTRACT: We construct families of digital (t,m,s)-nets over F4 improving the best known parameters of (t,m,s)-nets. We also improve the bound of Niederreiter and Xing in the asymptotic theory of digital (t,m,s)-nets.
    Preview · Article · Jul 2008 · Finite Fields and Their Applications
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    • "Again, better bounds exist for small values of q. Namely, c(3, 6) ≤ 2.5 [6] and c(4, 6) ≤ 17/6 [10]. We summarize the bounds described so far inFigure 1. "
    [Show abstract] [Hide abstract] 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 ρ(q,n,d)=n-log q A(q,n,d) 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 ρ(q,n,d)≤((d-3)+1/(d-2))log q n 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.
    Full-text · Article · Oct 2004 · IEEE Transactions on Information Theory
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    • "Again, better bounds exist for small values of q. Namely, c(3, 6) ≤ 2.5 [6] and c(4, 6) ≤ 17/6 [10]. We summarize the bounds described so far inFigure 1. "
    [Show abstract] [Hide abstract] 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 (q; n; d) = n log q A(q; n; d) 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 BCH codes and have the lowest asymptotic redundancy (q; n; d) . ((d 3) + 1=(d 2)) log q n 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.
    Full-text · Article · Jul 2004
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