Quantum Codes Obtained From Constacyclic Codes Over a Family of Finite Rings F_p[u₁, u₂, …, u_s]

Abstract

In this paper, we construct some MDS quantum error-correcting codes (QECCs) from classes of constacyclic codes over R s = F p + u 1 F p + • • • + u s F p , u 2 i = u i , u i u j = u j u i = 0, for odd prime p and i, j = 1, 2,. .. , s, i = j. Many QECCs with improved parameters than the existing ones in some of the earlier papers are provided. We present a set of idempotent generators of the ring R s , and using that we define linear codes, determine all units, and study constacyclic codes over this ring. Among others, we study dual containing constacyclic codes over R s and construct (non-binary) QECCs. An algorithm to construct QECCs from dual containing constacyclic codes over R s is obtained that can provide many quantum codes. INDEX TERMS Cyclic codes, negacyclic codes, constacyclic codes, quantum codes.

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