Complete Weight Enumerator for a Class of Linear Codes from Defining Sets and Their Applications

被引：3
作者：
Liu, Haibo
Liao, Qunying [1 ]
Wang, Xiaofeng [2 ]
机构：
[1] Sichuan Normal Univ, Inst Math & Software Sci, Chengdu 610066, Sichuan, Peoples R China
[2] Shenzhen Univ, Coll Math & Stat, Shenzhen 518061, Peoples R China
来源：
JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY | 2019年 / 32卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Authentication codes; complete weight enumerator; constant composition codes; exponential sums; linear codes; secret sharing schemes; weight distributions;
D O I：
10.1007/s11424-018-7414-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Recently, linear codes over finite fields with a few weights have been extensively studied due to their applications in secret sharing schemes, authentication codes, constant composition codes. In this paper, for an odd prime p, the complete weight enumerator of a class of p-ary linear codes based on defining sets are determined. Furthermore, from the explicit complete weight enumerator of linear codes, a new class of optimal constant composition codes and several classes of asymptotically optimal systematic authentication codes are obtained.
引用
收藏
页码：947 / 969
页数：23
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