One and Two‐Weight ℤ ₂ R ₂ Additive Codes

Abstract

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 Z2R2 and its dual is established. Several construction methods of one‐weight and two‐weight additive codes over Z2R2 are presented. Several examples are presented to illustrate our main results and some open problems are also proposed.