Constacyclic codes over F^q2[u]/⟨^u2-^w2⟩ and their application in quantum code construction

Abstract

Let q be an odd prime power, and w be a generator of the multiplicative cyclic group Fq2∗. In this work, we study constacyclic codes over R=Fq2+uFq2(u2=w2), and show a construction of quantum codes by studying the Hermitian construction over R. To do that, we discuss the σ-inner product over any finite commutative Frobenius ring and using that we define the Hermitian inner product over R. We decompose the ring R by constructing a pairwise orthogonal idempotent and study linear codes. We present the units of R and using them we study constacyclic codes and their generators over R. We also provide a condition for a constacyclic code to contain its Hermitian dual over this ring. Finally, we constructed some codes, which have improved parameters than some of the recently constructed codes in the literature. We also present a table of codes, which have better parameters than those currently available in the online database.