MINERALOGIE ŽELEZNÝCH RUD Z ROZVODNÉHO VRCHU U ČABOVÉ VE STŘEDNÍ ČÁSTI ŠTERNBERSKO-HORNOBENEŠOVSKÉHO PRUHU (MORAVSKOSLEZSKÁ JEDNOTKA ČESKÉHO MASIVU)

On $\mathbb{Z}_{2}\mathbb{Z}_{2}[u]$-$(1+u)$-additive constacyclic

In this paper, we study Z2Z2[u]-(1 + u)-additive constacyclic code of arbitrary length. Firstly, we study the algebraic structure of this family of codes and a set of generator polynomials for this family as a (Z2+uZ2)[x]-submodule of the ring Rα,β. Secondly, we give the minimal generating sets of this family codes, and we determine the relationship of generators between the Z2Z2[u]-(1 + u)-add...

$\mathbb{Z}_p\mathbb{Z}_p[u]$-additive codes

Abstract: In this paper, we study ZpZp[u]-additive codes, where p is prime and u 2 = 0. In particular, we determine a Gray map from ZpZp[u] to Z α+2β p and study generator and parity check matrices for these codes. We prove that a Gray map Φ is a distance preserving map from (ZpZp[u],Gray distance) to (Z α+2β p ,Hamming distance), it is a weight preserving map as well. Furthermore we study the ...

Cyclic codes over $\mathbb{Z}_4+u\mathbb{Z}_4$

In this paper, we have studied cyclic codes over the ring R = Z4 +uZ4, u = 0. We have considered cyclic codes of odd lengths. A sufficient condition for a cyclic code over R to be a Z4-free module is presented. We have provided the general form of the generators of a cyclic code over R and determined a formula for the ranks of such codes. In this paper we have mainly focused on principally gene...

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Self-Dual Codes over $\mathbb{Z}_2\times (\mathbb{Z}_2+u\mathbb{Z}_2)$

In this paper, we study self-dual codes over Z2× (Z2+uZ2), where u 2 = 0. Three types of self-dual codes are defined. For each type, the possible values α, β such that there exists a code C ⊆ Z2×(Z2+uZ2) β are established. We also present several approaches to construct self-dual codes over Z2 × (Z2 + uZ2). Moreover, the structure of two-weight self-dual codes is completely obtained for α · β 6...