Minimal linear codes constructed from functions

被引：6

作者：

Wu, Xia ^{[1
]}

Lu, Wei ^{[1
]}

Cao, Xiwang ^{[2
]}

机构：

[1] Southeast Univ, Sch Math, Nanjing 210096, Peoples R China

[2] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 211100, Peoples R China

来源：

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2022年 / 14卷 / 04期

关键词：

Linear code; Minimal code; q-ary function; Maiorana-McFarland functions; Secret sharing; 2-WEIGHT; FAMILIES; WEIGHTS;

D O I：

10.1007/s12095-021-00553-4

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this paper, we consider minimal linear codes by a general construction of linear codes from q-ary functions. First, we give necessary and sufficient conditions for codewords which are constructed by functions to be minimal. Second, as applications, we present three constructions of minimal linear codes. Constructions on minimal linear codes in this paper generalize some recent results in Ding et al. (IEEE Trans. Inf. Theory 64(10), 6536-6545, 2018); Heng et al. (Finite Fields Appl. 54, 176-196, 2018); Bartoli and Bonini (IEEE Trans. Inf. Theory 65(7), 4152-4155, 2019); Mesnager et al. (IEEE Trans. Inf. Theory 66(9), 5404-5413, 2020); Bonini and Borello (J. Algebraic Comb. 53, 327-341, 2021). In our three constructions, the conditions of functions are much looser than theirs.

引用

页码：875 / 895

页数：21

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