2025, Vol. 10, Issue 8, Part C

The structural properties and construction methodologies of quantum codes (QCs) defined over the finite field Z_3, the finite field with three elements, are examined in this work. The primary focus is on utilizing constacyclic codes within a specific algebraic structure the finite commutative non-chain ring R=Z₃+uZ₃+vZ₃+uvZ₃, where the indeterminates u and v satisfy the relations u²=1, v²=1, and uv=vu. We provide a set of idempotent generators of the ring and define linear codes and calculated some self-inverse units. The relationship between R and Z₃⁴ is established using a gray map. Constacyclic (CC) codes are broken down into cyclic (C) codes and negacyclic (N) codes in order to determine the parameters of QCs over Z_3. Several QCs of arbitrary lengths are developed as an application. In this paper, we calculated those various parameters of QCs which are better than existing parameters of QCs. This paper contains only those units which have self-inverse.