For any prime number p, positive integers m, k, n satisfying gcd(p, n) = 1 and λ0 ∈ F × pm, we prove that any λ p 0 -constacyclic code of length p n over the finite field Fpm is monomially equivalent to a matrix-product code of a nested sequence of p λ0-constacyclic codes with length n over Fpm.

In this paper we generalize the notion of cyclicity of codes, that is, θ-polycyclic codes and θ-sequential codes. It is shown that for a code C, C is θ-polycyclic (θ-sequential) if and only if its dual C⊥ is θ−1-sequential (θ−1-polycyclic). Furthermore, we study central θ-constacyclic codes. Mathematics Subject Classification: Primary 94B60; Secondary 94B15, 16W20

We introduce circulant matrices that capture the structure of a skew-polynomial ring F[x; θ] modulo the left ideal generated by a polynomial of the type x − a. This allows us to develop an approach to skew-constacyclic codes based on such circulants. Properties of these circulants are derived, and in particular it is shown that the transpose of a certain circulant is a circulant again. This rec...

Constacyclic codes may naturally be viewed as objects arising from the cohomological concept of a cocycle. Cohomology theory suggests a transformation which is used to show, under certain circumstances, a cyclic code of length mn over a ring R is isomorphic to the direct sum of m constacyclic codes of length n. In particular this isomorphism holds in many local rings (for example Galois rings) ...

Using geometric properties of the variety Vr,t, the image under the Grassmannian map of a Desarguesian (t− 1)-spread of PG (rt− 1, q), we introduce error correcting codes related to the twisted tensor product construction, producing several families of constacyclic codes. We exactly determine the parameters of these codes and characterise the words of minimum weight.

In this paper a family of constacyclic ternary quasi-perfect linear block codes is presented. This family extends the result presented in a previous work by the first two authors, where the existence of codes with the presented parameters was stated as an open question. The codes have a minimum distance 5 and covering radius 3.