TY - JOUR
T1 - Distance bounds for algebraic geometric codes
AU - Duursma, Iwan
AU - Kirov, Radoslav
AU - Park, Seungkook
PY - 2011/8
Y1 - 2011/8
N2 - 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 Güneri, 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.
AB - 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 Güneri, 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.
UR - http://www.scopus.com/inward/record.url?scp=79952485065&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79952485065&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2010.10.018
DO - 10.1016/j.jpaa.2010.10.018
M3 - Article
AN - SCOPUS:79952485065
SN - 0022-4049
VL - 215
SP - 1863
EP - 1878
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 8
ER -