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

In this article, 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
_i
²
= 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 Rs, 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 Rs and construct (non-binary) QECCs. An algorithm to construct QECCs from dual containing constacyclic codes over Rs is obtained that can provide many quantum codes.