There is exactly one Z2Z4-cyclic 1-perfect code

被引：0
|
作者：
Borges, Joaquim [1 ]
Fernandez-Cordoba, Cristina [1 ]
机构：
[1] Univ Autonoma Barcelona, Dept Informat & Commun Engn, Cerdanyola Del Valles 08193, Spain
来源：
DESIGNS CODES AND CRYPTOGRAPHY | 2017年 / 85卷 / 03期
关键词：
Perfect codes; Z(2)Z(4)-additive cyclic codes; Simplex codes;
D O I：
10.1007/s10623-016-0323-3
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Let C be a Z(2)Z(4)-additive code of length n > 3. We prove that if the binary Gray image of C is a 1-perfect nonlinear code, then C cannot be a Z(2)Z(4)-cyclic code except for one case of length n = 15. Moreover, we give a parity check matrix for this cyclic code. Adding an even parity check coordinate to a Z(2)Z(4)-additive 1-perfect code gives a Z(2)Z(4)-additive extended 1-perfect code. We also prove that such a code cannot be Z(2)Z(4)-cyclic.
引用
收藏
页码：557 / 566
页数：10
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