LAUSR

In this paper, for q = pm (p is prime) such that q ≡ 1 (mod e), we study skew constacyclic codes over a class of non-chain rings $R_{e,q}=\mathbb {F}_{q}[u]/\langle u^{e}-1\rangle $ where m, e ≥ 2 are integers. We decompose the ring into a direct sum of local rings, and consequently, skew constacyclic codes over that ring into a direct sum of skew constacyclic codes over local rings. This decomposition yields the structure of Euclidean duals of skew constacyclic codes and further a necessary and sufficient condition to contain their duals. From an application point of view, we apply the CSS (Calderbank-Shor-Steane) construction on Gray images of dual containing skew constacyclic codes and obtain many quantum codes improving the best-known codes in the literature.