One and Two-Weight \mathbbZ_2R_2 Additive Codes

LI Tiantian; SHI Minjia; LIN Bo; WU Wenting

doi:10.1049/cje.2020.10.011

LI Tiantian, SHI Minjia, LIN Bo, WU Wenting. One and Two-Weight $\mathbb{Z}_{2}R_{2}$ Additive Codes[J]. Chinese Journal of Electronics, 2021, 30(1): 72-76. DOI: 10.1049/cje.2020.10.011

Citation:

LI Tiantian, SHI Minjia, LIN Bo, WU Wenting. One and Two-Weight $\mathbb{Z}_{2}R_{2}$ Additive Codes[J]. Chinese Journal of Electronics, 2021, 30(1): 72-76. DOI: 10.1049/cje.2020.10.011

Citation:

LI Tiantian, SHI Minjia, LIN Bo, WU Wenting. One and Two-Weight $\mathbb{Z}_{2}R_{2}$ Additive Codes[J]. Chinese Journal of Electronics, 2021, 30(1): 72-76. DOI: 10.1049/cje.2020.10.011

One and Two-Weight \mathbbZ_2R_2 Additive Codes

Graphical Abstract

Graphical Abstract

Abstract

Abstract

This paper is devoted to the construction of one and two-weight \mathbbZ_2R_2 additive codes, where R_2=\mathbbF_2v/\langle v.4\rangle. It is a generalization towards another direction of \mathbbZ_2\mathbbZ_4 codes (S.T. Dougherty, H.W. Liu and L. Yu, "One weight \mathbbZ_2\mathbbZ_4 additive codes", \textitApplicable 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 \mathbbZ_2R_2 and its dual is established. Several construction methods of one-weight and two-weight additive codes over \mathbbZ_2R_2 are presented. Several examples are presented to illustrate our main results and some open problems are also proposed.