Linear Codes and Linear Complementary Pairs of Codes Over a Non-Chain Ring

Let p be an odd prime number, q = p(m) for a positive integer m, let F(q )be the finite field with q elements and omega be a primitive element of Fq. We first give an orthogonal decomposition of the ring R = F-q + nu F-q, where nu(2) = a(3), and a = omega(2l )for a fixed integer l. In addition, Galois dual of a linear code over R is discussed. Meanwhile, constacyclic codes and cyclic codes over the ring R are investigated as well. Remarkably, we obtain that if linear codes C and D are a complementary pair, then the code C and the dual code D-&updatedExpOTTOM;E of D are equivalent to each other.