2010/01/08 by Iwan Duursma, Duursma, Iwan, Radoslav Kirov +3
Computer Science · Mathematics · #11T71 #14G50 #94B #Algebraic Geometry (math.AG) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #cs.IT #math.AG #math.IT #msc:11T71 #msc:14G50 #msc:94B
paper · pdf · doi:10.48550/arxiv.1001.1374
29 pages
arxiv created 2010/01/08 · arxiv updated 2010/01/14
Various methods have been used to obtain improvements of the Goppa lower bound for the minimum distance of an algebraic geometric code. The main methods divide into two categories and all but a few of the known bounds are special cases of either the Lundell-McCullough floor bound or the Beelen order bound. The exceptions are recent improvements of the floor bound by Guneri-Stichtenoth-Taskin, and Duursma-Park, and of the order bound by Duursma-Park and Duursma-Kirov. In this paper we provide short proofs for all floor bounds and most order bounds in the setting of the van Lint and Wilson AB method. Moreover, we formulate unifying theorems for order bounds and formulate the DP and DK order bounds as natural but different generalizations of the Feng-Rao bound for one-point codes.