ON QUANTUM CODES CONSTRUCTION FROM CONSTACYCLIC CODES OVER THE RING I_q[u,v] / - Ali, Shakir; Sharma, Pushpendra (IndoMS, 2024)
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=I_q[u,v]/u^2-α^2, v^2-α^2, uv-vu , where I_q is a finite field of q elements, α be the nonzero elements of the field I_q and q is a power of an odd prime p such that q=p^m, 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 I_q. 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).