VARIOUS STRUCTURES OF CYCLIC CODES OVER THE NON-FROBENIUS RING Fp[u, v]/>au2, v2, uv, vu5b

. In this paper, we study cyclic codes over the ring Rp = Fp+uFp+ vFp, where u2 = v2 = uv = vu = 0 (p: a prime number). We first derive generators of ideals of Rp[x]/(xn - 1), which are corresponding to cyclic codes over Rp of arbitrary length n. Especially, for gcd(n, p) = 1, we have the explicit generators of ideals corresponding to cyclic codes, their duals, self-orthogonal codes and self-dual codes over Rp of length n. Furthermore, mass formulae of cyclic self-orthogonal and LCD codes over Rp of length n is obtained. Finally, we present a Gray map from (Rp)n to (Fp)6n, showing that the image of a cyclic code over this Gray map is quasi-cyclic, and determine the index of this image. A series of examples and tables concerning the mass formula of cyclic self-orthogonal codes, cyclic LCD codes and several new quasi-cyclic codes are presented as an application of theorems.