On linear codes over a non-chain extension of F2 + uF2

Abstract

In this paper we study linear codes over a new ring R = F₂ + uF₂ + vF₂ + uvF₂ with u² = 0, v² = v and uv = vu, which is a non chain extension of the ring F₂+uF₂, u² =0. We have obtained Mac Williams identities for Lee weight enumerator of linear codes over R using a Gray map from Rⁿ to (F₂ +uF₂)ⁿ. We have studied self-dual codes over R and determined some existential conditions for Type I and Type II codes over R. Further we have briefly studied cyclic codes over R. It is shown that R[x]/〈xⁿ - 1〉 is a PIR when n is odd. The form of the generator of a cyclic code of odd length over R is obtained.