ON QUANTUM CODES CONSTRUCTION FROM CONSTACYCLIC CODES OVER THE RING I_q[u,v] / <u^2-a^2, v^2-a^2, uv-vu>

This paper focuses on studying the properties of constacyclic codes, quantum error-correcting codes. The code is studied over a specific mathematical structure called the ring S, which is defined as S=Iq[u,v]/ u²-α²,~ v²-α²,~uv-vu, where Iq is a finite field of q elements, α be the nonzero elements of the field Iq and q is a power of an odd prime p such that q=pᵐ, ~for~ m ≥ 1. The paper also introduces a Gray map and use it to decompose constacyclic codes over the ring S into a direct sum of constacyclic codes over Iq. We construct new and better quantum error-correcting codes over the ring S (cf.; Table 1 and Table 2). Moreover, we also obtain best known linear codes as well as best dimension linear codes (cf.; Table 4).