Optimal Few-Weight Codes From Simplicial Complexes

被引：22
|
作者：
Wu, Yansheng [1 ,2 ,3 ]
Zhu, Xiaomeng [1 ,2 ]
Yue, Qin [1 ,2 ]
机构：
[1] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 211100, Peoples R China
[2] State Key Lab Cryptol, Beijing 100878, Peoples R China
[3] Ewha Womans Univ, Dept Math, Seoul 03760, South Korea
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2020年 / 66卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Few-weight codes; codes over rings; simplicial complexes; Griesmer bound; LINEAR CODES; TRACE CODES; 2-WEIGHT;
D O I：
10.1109/TIT.2019.2946840
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
Recently, some infinite families of binary minimal and optimal linear codes were constructed from simplicial complexes by Hyun et al. Inspired by their work, we present two new constructions of codes over the ring F-2 + uF(2) by employing simplicial complexes. When the simplicial complexes are all generated by a maximal element, we determine the Lee weight distributions of two classes of the codes over F-2 + uF(2). Our results show that the codes have few Lee weights. Via the Gray map, we obtain an infinite family of binary codes meeting the Griesmer bound and a class of binary distance optimal codes.
引用
收藏
页码：3657 / 3663
页数：7
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