Some bounds on binary LCD codes

被引：62

作者：

Galvez, Lucky ^{[1
]}

Kim, Jon-Lark ^{[1
]}

Lee, Nari ^{[1
]}

Roe, Young Gun ^{[1
]}

Won, Byung-Sun ^{[1
]}

机构：

[1] Sogang Univ, Dept Math, Seoul 04107, South Korea

来源：

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2018年 / 10卷 / 04期

基金：

新加坡国家研究基金会;

关键词：

Binary LCD codes; Bounds; Linear codes; LINEAR CODES; COMPLEMENTARY;

D O I：

10.1007/s12095-017-0258-1

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

A linear code with a complementary dual (or An LCD code) is defined to be a linear code C whose dual code C-perpendicular to satisfies C boolean AND C-perpendicular to={0}. Let LD(n, k) denote the maximum of possible values of d among [n, k, d] binary LCD codes. We give the exact values of LD(n, k) for k = 2 for all n and some bounds on LD(n, k) for other cases. From our results and some direct search we obtain a complete table for the exact values of LD(n, k) for 1 <= k <= n <= 12. As a consequence, we also derive bounds on the dimensions of LCD codes with fixed lengths and minimum distances.

引用

页码：719 / 728

页数：10

共 24 条

[1] The principal rank characteristic sequence over various fields [J].