One and Two-Weight Z2R2 Additive Codes

• 作者: LI Tiantian SHI Minjia LIN Bo WU Wenting
• 来源期刊: 电子学报（英文）
• 年，卷（期）: 2021,（1）
• 所属期刊栏目: COMPUTERS AND MICROELECTRONICS
• 页码范围: 72-76
• 页数: 5页
• 语种: 英文
• DOI: 10.1049/cje.2020.10.011

摘要

This paper is devoted to the construction of one and two-weight Z2R2 additive codes, where R2 =F2[v]/<v4>. It is a generalization towards another direction of Z2Z4 codes (S.T. Dougherty, H.W. Liu and L. Yu,"One weight Z2Z4 additive codes", Applicable Algebra in Engineering, Communication and Computing, Vol.27, No.2, pp.123–138, 2016). A MacWilliams identity which connects the weight enumerator of an additive code over Z2 R2 and its dual is established. Several construction methods of one-weight and two-weight additive codes over Z2 R2 are presented. Several examples are presented to illustrate our main results and some open problems are also proposed.