We study constacyclic codes, of length np and 2np, that are generated by the polynomials (x+γ) and (x−ξ)(x+ξ) respectively, where x+γ, x−ξ and x+ξ are irreducible over the alphabet Fpa . We generalize the results of [5], [6] and [7] by computing the minimum Hamming distance of these codes. As a particular case, we determine the minimum Hamming distance of cyclic and negacyclic codes, of length ...

In this paper, we study the algebraic structure of Z2[u]Z2[u, v]-additive codes which are Z2[u, v]-submodules where u 2 = v2 = 0 and uv = vu. In particular, we determine a Gray map from Z2[u]Z2[u, v] to Z 2α+8β 2 and study generator and parity check matrices for these codes. Further we study the structure of Z2[u]Z2[u, v]additive cyclic codes and constacyclic codes.

For any different odd primes ` and p, structure of constacyclic codes of length 2`p over the finite field Fq of characteritic p and their duals is established in term of their generator polynomials. Among other results, the characterization and enumeration of all linear complimentary dual and self-dual constacylic codes of length 2`p are obtained.

We show how cyclic (f, σ, δ)-codes over finite rings canonically induce a Z-lattice in R N. The construction can be viewed as a generalization of the classical Construction A for lattices from linear codes and has applications to coset coding, in particular to wire-tap coding. Previous results for lattices obtained from σ-constacyclic codes by Ducoat and Oggier are obtained as special cases.