Classification of Extremal and s-Extremal Binary Self-Dual Codes of Length 38

被引：12

作者：

Aguilar-Melchor, Carlos ^{[1
]}

Gaborit, Philippe ^{[1
]}

Kim, Jon-Lark ^{[2
]}

Sok, Lin ^{[3
]}

Sole, Patrick ^{[4
,5
]}

机构：

[1] Univ Limoges, XLIM DMI, UMR 6172, F-87000 Limoges, France

[2] Univ Louisville, Dept Math, Louisville, KY 40292 USA

[3] Telecom ParisTech, Dept Comelec, F-75013 Paris, France

[4] Telecom ParisTech, CNRS LTCI, UMR 5141, F-75634 Paris 13, France

[5] King Abdulaziz Univ, Dept Math, MECAA, Jeddah, Saudi Arabia

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2012年 / 58卷 / 04期

关键词：

Classification; extremal; recursive construction; self-dual codes; s-extremal; shadow; LATTICES;

D O I：

10.1109/TIT.2011.2177809

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper we classify all extremal and s-extremal binary self-dual codes of length 38. There are exactly 2744 extremal [38, 19, 8] self-dual codes, two s-extremal [38, 19, 6] codes, and 1730 s-extremal [38, 19, 8] codes. We obtain our results from the use of a recursive algorithm used in the recent classification of all extremal self-dual codes of length 36, and from a generalization of this recursive algorithm for the shadow. The classification of s-extremal [38, 19, 6] codes permits to achieve the classification of all s-extremal codes with d = 6.

引用

页码：2253 / 2262

页数：10

共 25 条

[1] Designs and self-dual codes with long shadows [J].