In this paper we will study cyclic codes over some special rings: Fq[u]/(u ),Fq[u1, ..., ui]/(u 2 1, u 2 2, ..., u 2 i , u1u2 − u2u1, ..., ukuj − ujuk, ...), Fq[u, v]/ ( u, v , uv − vu ) , q = p, where p is a prime number, r ∈ N−{0} and Fq is a field with q elements.

In this paper, we study cyclic stabiliser codes over Fp of length dividing p + 1 for some positive integer t. We call these t-Frobenius codes or just Frobenius codes for short. We give methods to construct them and show that they have efficient decoding algorithms. An important subclass of stabiliser codes are the linear stabiliser codes. For linear Frobenius codes we have stronger results: We ...

We present a family of reducible cyclic codes constructed as a direct sum (as vector spaces) of two different semiprimitive two-weight irreducible cyclic codes. This family generalizes the class of reducible cyclic codes that was reported in the main result of [10]. Moreover, despite of what was stated therein, we show that, at least for the codes studied here, it is still possible to compute t...

In this paper, a family of reducible cyclic codes over Fp whose duals have four zeros is presented, where p is an odd prime. Furthermore, the weight distribution of these cyclic codes is determined.

In this paper we will study the weight distribution of some cyclic codes which have several non zeroes only.

In this paper, a family of six-weight cyclic codes over Fp whose duals have three zeros is presented, where p is an odd prime. And the weight distribution of these cyclic codes is determined.

In this paper, we study skew cyclic codes over the ring R = Fq + uFq + vFq + uvFq, where u 2 = u, v2 = v, uv = vu, q = p and p is an odd prime. We investigate the structural properties of skew cyclic codes over R through a decomposition theorem. Furthermore, we give a formula for the number of skew cyclic codes of length n over R.

We introduce linear cyclic codes over the ring F 2 + uF 2 = f0; 1; u; u = u + 1g, where u 2 = 0. This ring shares many properties of Z 4 and F 4 and admits a linear "Gray map". Cyclic codes are described as modules over (F 2 + uF 2) n which may not be free. Self-dual codes of odd length exists as in the case of Z 4-codes. We exhibit some extremal codes of this very interesting family.

In this paper, a family of five-weight cyclic codes over Fp whose duals have three zeros is presented, where p is an odd prime. And the weight distribution of these cyclic codes is determined.