Skew constacyclic codes over a class of finite commutative semisimple rings

In this article, we study skew constacyclic codes over a class of finite commutative semisimple rings. The automorphism group of $\mathcal{R}=\prod_{i=1}^t F_q$ is determined, and we characterize skew constacyclic codes over ring by linear codes over finite field. We also define homomorphisms which map linear codes over $\mathcal{R}$ to matrix product codes over $F_q,$ some optimal linear codes over finite fields are obtained.

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