Optimal p-ary cyclic codes with minimum distance four from monomials

被引：28
|
作者：
Xu, Guangkui [1 ,2 ]
Cao, Xiwang [1 ,3 ]
Xu, Shanding [1 ,4 ]
机构：
[1] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Jiangsu, Peoples R China
[2] Huainan Normal Univ, Dept Appl Math, Huainan 232038, Peoples R China
[3] Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China
[4] Nanjing Inst Technol, Dept Math & Phys, Nanjing 210016, Jiangsu, Peoples R China
来源：
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES | 2016年 / 8卷 / 04期
关键词：
Cyclic code; Perfect nonlinear function; Almost perfect nonlinear function; Finite field; PERFECT NONLINEAR FUNCTIONS; LINEAR CODES; WEIGHT DISTRIBUTIONS; POWER FUNCTIONS; APN FUNCTIONS; SEMIFIELDS; MAPPINGS; FAMILIES;
D O I：
10.1007/s12095-015-0159-0
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
For any odd prime p >= 5, some optimal p-ary cyclic codes with parameters [p(m)-1, p(m)-2m-2,4] are presented by using perfect nonlinear monomials and the inverse function over F-pm. In addition, almost perfect nonlinear monomials, and other monomials over F-5m are used to construct optimal quinary cyclic codes with parameters [5(m) -1, 5(m) - 2m -2, 4].
引用
收藏
页码：541 / 554
页数：14
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