Linear codes with few weights from weakly regular bent functions based on a generic construction

被引：72
|
作者：
Mesnager, Sihem [1 ,2 ]
机构：
[1] Univ Paris XIII, Univ Paris VIII, CNRS, Dept Math,LAGA,UMR 7539, Paris, France
[2] Telecom ParisTech, Paris, France
来源：
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2017年 / 9卷 / 01期
关键词：
Linear codes; p-ary codes; Weight distribution; p-ary functions; Bent functions; Weakly regular bent functions; Vectorial functions; Cyclotomic fields; Secret sharing schemes; CYCLIC CODES; NONLINEAR FUNCTIONS; 3-WEIGHT CODES; FINITE-FIELDS;
D O I：
10.1007/s12095-016-0186-5
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
We contribute to the knowledge of linear codes with few weights from special polynomials and functions. Substantial efforts (especially due to C. Ding) have been directed towards their study in the past few years. Such codes have several applications in secret sharing, authentication codes, association schemes and strongly regular graphs. Based on a generic construction of linear codes from mappings and by employing weakly regular bent functions, we provide a new class of linear p-ary codes with three weights given with its weight distribution. The class of codes presented in this paper is different from those known in literature.
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收藏
页码：71 / 84
页数：14
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