Designs in additive codes over GF(4)

被引：23

作者：

Kim, JL

Pless, V

机构：

[1] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA

[2] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2003年 / 30卷 / 02期

关键词：

additive code; Assmus-Mattson theorem; generalized t-design;

D O I：

10.1023/A:1025484821641

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The purpose of this paper is to study designs in additive codes over GF(4). There are two types of designs. One is a classical t-design with repeated blocks. In this case we have an analog of the Assmus Mattson Theorem for additive codes over GF(4). The other is a generalized t-design first introduced by Delsarte [4]. As an example, we consider the dodecacode, which is the unique additive even self-dual (12; 2(12); 6) code. We show that there exists a 5-(12, 6, 3) design in the dodecacode with either 3 distinct blocks or 3 repeated blocks covering a 5- set. We also find a new simple 3-(11, 5, 4) design in the shortened dodecacode by a computer search. Additionally we show that any extremal additive even self-dual code over GF(4) is homogeneous.

引用

页码：187 / 199

页数：13