Related papers: On the Kernel of $\Z_{2^s}$-Linear Simplex and Mac…
In this paper we define $\mathbb{Z}_{2}\mathbb{Z}_{4}-$Simplex and MacDonald Codes of type $\alpha $ and $\beta $ and we give the covering radius of these codes.
Self-dual codes over $\Z_2\times\Z_4$ are subgroups of $\Z_2^\alpha \times\Z_4^\beta$ that are equal to their orthogonal under an inner-product that relates to the binary Hamming scheme. Three types of self-dual codes are defined. For each…
A binary linear code $C$ is a $\mathbb{Z}_2$-double cyclic code if the set of coordinates can be partitioned into two subsets such that any cyclic shift of the coordinates of both subsets leaves invariant the code. These codes can be…
A Z2Z4-additive code C subset of Z_2^alpha x Z_4^beta is called cyclic if the set of coordinates can be partitioned into two subsets, the set of Z_2 and the set of Z_4 coordinates, such that any cyclic shift of the coordinates of both…
A linear code of length $n$ over a finite chain ring $R$ with residue field $\F_q$ is a $R$-submodule of $R^n$. A $R$-linear code is a code over $\F_q$ (not necessarily linear) which is the generalized Gray map image of a linear code over…
A classic result of Delsarte connects the strength (as orthogonal array) of a linear code with the minimum weight of its dual: the former is one less than the latter. We show that Delsarte's observation extends to codes over arbitrary…
In this article we mainly study linear codes over $\mathbb{F}_{2^n}$ and their binary subfield codes. We construct linear codes over $\mathbb{F}_{2^n}$ whose defining sets are the certain subsets of $\mathbb{F}_{2^n}^m$ obtained from…
The well known Plotkin construction is, in the current paper, generalized and used to yield new families of Z2Z4-additive codes, whose length, dimension as well as minimum distance are studied. These new constructions enable us to obtain…
An alternative permutation decoding method is described which can be used for any binary systematic encoding scheme, regardless whether the code is linear or not. Thus, the method can be applied to some important codes such as Z2Z4-linear…
In this paper, we study the algebraic structure of Z_2[u]Z_2[u, v]-additive codes which are Z_2[u, v]-submodules where u^2 = v^2 = 0 and uv = vu. In particular, we determine a Gray map from Z_2[u]Z_2 [u, v] to Z_2^{2{\alpha}+8\b{eta}} and…
Recently some mixed alphabet rings are involved in constructing few-Lee weight additive codes with optimal or minimal Gray images using suitable defining sets or down-sets. Inspired by these works, we choose the mixed alphabet ring…
In this paper we study $\prod\limits_{i=1}^{n} \mathbb{Z}_{2^i}$-Additive Cyclic Codes. These codes are identified as $\mathbb{Z}_{2^n}[x]$-submodules of $\prod\limits_{i=1}^{n}\mathbb{Z}_{2^i}[x]/ \langle x^{\alpha_i}-1\rangle$; $\alpha_i$…
Recently, simplicial complexes are used in constructions of several infinite families of minimal and optimal linear codes by Hyun {\em et al.} Building upon their research, in this paper more linear codes over the ring $\mathbb{Z}_4$ are…
A complementary Gray code for binary n-tuples is one that, when all the tuples are complemented, is identical to itself; this is equivalent to the complement of the first half of the code being identical to the second half. We generalize…
Linear complementary dual codes (or codes with complementary duals) are codes whose intersections with their dual codes are trivial. We study binary linear complementary dual $[n,k]$ codes with the largest minimum weight among all binary…
Certain notorious nonlinear binary codes contain more codewords than any known linear code. These include the codes constructed by Nordstrom-Robinson, Kerdock, Preparata, Goethals, and Delsarte-Goethals. It is shown here that all these…
We consider codes over $\mathbb{Z}_{p^s}$ with the extended Lee weight. We find Singleton bounds with respect to this weight and define MLDS and MLDR codes accordingly. We also consider the kernels of these codes and the notion of…
A ${\mathbb{Z}}_2{\mathbb{Z}}_4$-additive code ${\cal C}\subseteq{\mathbb{Z}}_2^\alpha\times{\mathbb{Z}}_4^\beta$ is called cyclic if the set of coordinates can be partitioned into two subsets, the set of ${\mathbb{Z}}_2$ and the set of…
For each r, 0 <= r <= m, it is presented the class of quaternary linear codes LRM(r,m) whose images under the Gray map are binary codes with parameters of Reed-Muller RM(r,m) code of order r.
A code $C = \Phi(\mathcal{C})$ is called $\mathbb{Z}_p \mathbb{Z}_{p^2}$-linear if it's the Gray image of the $\mathbb{Z}_p \mathbb{Z}_{p^2}$-additive code $\mathcal{C}$. In this paper, the rank and the dimension of the kernel of…