Self-Dual Codes over $\mathbb{Z}_2\times (\mathbb{Z}_2+u\mathbb{Z}_2)$
نویسندگان
چکیده
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= 0.
منابع مشابه
One-Lee weight and two-Lee weight $\mathbb{Z}_2\mathbb{Z}_2[u]$-additive codes
In this paper, we study one-Lee weight and two-Lee weight codes over Z2Z2[u], where u = 0. Some properties of one-Lee weight Z2Z2[u]-additive codes are given, and a complete classification of one-Lee weight Z2Z2[u]-additive formally self-dual codes is obtained. The structure of two-Lee weight projective Z2Z2[u] codes are determined. Some optimal binary linear codes are obtained directly from on...
متن کاملOn cyclic DNA codes over $\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2$
In the present paper we study the structure of cyclic DNA codes of even length over the ring F2 + uF2 + u 2 F2 where u 3 = 0. We investigate two presentations of cyclic codes of even length over F2 + uF2 + u 2 F2 satisfying the reverse constraint and the reverse-complement constraint.
متن کاملRelative two-weight $\mathbb{Z}_2 \mathbb{Z}_4$-additive Codes
In this paper, we study a relative two-weight Z2Z4-additive codes. It is shown that the Gray image of a two-distance Z2Z4-additive code is a binary two-distance code and that the Gray image of a relative two-weight Z2Z4-additive code, with nontrivial binary part, is a linear binary relative two-weight code. The structure of relative two-weight Z2Z4-additive codes are described. Finally, we disc...
متن کاملComputing the generator polynomials of $\mathbb{Z}_2\mathbb{Z}_4$-additive cyclic codes
A Z2Z4-additive code C ⊆ Z α 2 × Z β 4 is called cyclic if the set of coordinates can be partitioned into two subsets, the set of Z2 and the set of Z4 coordinates, such that any simultaneous cyclic shift of the coordinates of both subsets leaves invariant the code. These codes can be identified as submodules of the Z4[x]-module Z2[x]/(x − 1)×Z4[x]/(x −1). Any Z2Z4-additive cyclic code C is of t...
متن کاملOn Quantum Codes Obtained From Cyclic Codes Over $\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2$
The aim of this paper is to develop the theory for constructing DNA cyclic codes of odd length over R = Z4[u]/〈u 2 − 1〉. Firstly, we relate DNA pairs with a special 16 element of ring R. Cyclic codes of odd length over R satisfy the reverse constraint and the reverse-complement constraint are discussed in this paper. We also study the GC-content of these codes and their deletion distance. The p...
متن کامل