Constacyclic codes over mixed alphabets and their applications in constructing new quantum codes

Abstract

Let p be an odd prime and m be a positive integer, q= pm, R= Fq+ uFq with u2= u, and S= Fq+ uFq+ vFq with u2= u, v2= v, uv= vu= 0 and Λ = (λ1, λ2, λ3) ∈ FqRS. In this paper, we study the algebraic structure of constacyclic codes over R and S. Further, we discuss the structure of FqRS-Λ -constacyclic codes of block length (α, β, γ). This family of codes can be viewed as S[ x] -submodules of Fq[x]⟨xα-λ1⟩×R[x]⟨xβ-λ2⟩×S[x]⟨xγ-λ3⟩. The generator polynomials of this family of codes are discussed. As application, we discuss the construction of quantum error-correcting codes (QECCs) from constacyclic codes over FqRS and obtain several new QECCs from this study.