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Distance bounds for algebraic geometric codes

Authors
박승국IWAN DUURSMARADOSLAV KIROV
Issue Date
Aug-2011
Publisher
ELSEVIER SCIENCE B.V.
Citation
JOURNAL OF PURE AND APPLIED ALGEBRA, v.215, no.8, pp.1863 - 1878
Journal Title
JOURNAL OF PURE AND APPLIED ALGEBRA
Volume
215
Number
8
Start Page
1863
End Page
1878
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/12521
DOI
10.1016/j.jpaa.2010.10.018
ISSN
0022-4049
Abstract
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, and Taskin, and by Duursma and Park, and of the order bound by Duursma and Park, and by Duursma and 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.
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