Polyadic Cyclic Codes over a Non-Chain Ring

Let f(u) and g(v) be two polynomials of degree k and l respectively, not both linear which split into distinct linear factors over Fq. Let be a finite commutative non-chain ring. In this paper, we study polyadic codes and their extensions over the ring R. We give examples of some polyadic codes which are optimal with respect to Griesmer type bound for rings. A Gray map is defined from which preserves duality. The Gray images of polyadic codes and their extensions over the ring R lead to construction of self-dual, isodual, self-orthogonal and complementary dual (LCD) codes over Fq. Some examples are also given to illustrate this.