Related papers: DNA Codes over the Ring $\mathbb{Z}_4 + w\mathbb{Z…
In this paper, we study self-dual codes over $\mathbb{Z}_2 \times (\mathbb{Z}_2+u\mathbb{Z}_2) $, where $u^2=0$. Three types of self-dual codes are defined. For each type, the possible values $\alpha,\beta$ such that there exists a code…
In this paper, several infinite families of codes over the extension of non-unital non-commutative rings are constructed utilizing general simplicial complexes. Thanks to the special structure of the defining sets, the principal parameters…
In this paper, new few weights linear codes over the local ring $R=\mathbb{F}_p+u\mathbb{F}_p+v\mathbb{F}_p+uv\mathbb{F}_p,$ with $u^2=v^2=0, uv=vu,$ are constructed by using the trace function defined over an extension ring of degree $m.$…
For odd length $n$, the cyclic codes construction over $\Re= \Z_4[v]/ \langle v^2-v \rangle$ is provided. The hulls of cyclic codes over $\Re$ are studied. The average $2$-dimension $E(n)$ of the hulls of cyclic codes over $\Re$ is also…
In this work, we study codes over the ring R_{k,m}=F_2[u,v]/<u^{k},v^{m},uv-vu>, which is a family of Frobenius, characteristic 2 extensions of the binary field. We introduce a distance and duality preserving Gray map from R_{k,m} to…
In this paper, the investigation on the algebraic structure of the ring $\frac{\mathbb{F}_q[v]}{\langle\,v^q-v\,\rangle}$ and the description of its automorphism group, enable to study the algebraic structure of codes and their dual over…
Skew polynomial rings over finite fields ([7] and [10]) and over Galois rings ([8]) have been used to study codes. In this paper, we extend this concept to finite chain rings. Properties of skew constacyclic codes generated by monic right…
The homogeneous metric can be viewed as a natural extension of the Hamming metric to finite chain rings. It distinguishes between three types of elements: zero, non-zero elements in the socle, and elements outside the socle. Since the…
We construct an infinite family of two-Lee-weight and three-Lee-weight codes over the non-chain ring $\mathbb{F}_p+u\mathbb{F}_p+v\mathbb{F}_p+uv\mathbb{F}_p,$ where $u^2=0,v^2=0,uv=vu.$ These codes are defined as trace codes. They have the…
This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous…
Error-correcting codes over sets, with applications to DNA storage, are studied. The DNA-storage channel receives a set of sequences, and produces a corrupted version of the set, including sequence loss, symbol substitution, symbol…
In this article, we construct infinite families of quaternary (that is, over the ring $\mathbb{Z}_4$) $\mathcal{C}_{D}$-codes, where the defining set $D$ is derived utilizing a two-generator simplicial complex, and determine their Lee…
Let $A(n, d)$ denote the maximum size of a binary code of length $n$ and minimum Hamming distance $d$. Studying $A(n, d)$, including efforts to determine it as well to derive bounds on $A(n, d)$ for large $n$'s, is one of the most…
This paper contributes to construct double circulant self-dual codes by sextic cyclotomy. Generator matrixes of a family of pure double circulant codes and a family of double circulant codes with boundary are formed from sextic cyclotomic…
Self-orthogonal codes are a subclass of linear codes that are contained within their dual codes. Since self-orthogonal codes are widely used in quantum codes, lattice theory and linear complementary dual (LCD) codes, they have received…
Motivated by applications in in-vivo DNA storage, we study codes for correcting duplications. A reverse-complement duplication of length $k$ is the insertion of the reversed and complemented copy of a substring of length $k$ adjacent to its…
Based on the theoretical neuroscience, G. Cotardo and A. Ravagnavi in \cite{CR} introduced a kind of asymmetric binary codes called combinatorial neural codes (CN codes for short), with a "matched metric" $\delta_{r}$ called asymmetric…
Let $m\geq 2$ be any natural number and let $\mathcal{R}=\mathbb{F}_{p}+u\mathbb{F}_{p}+u^2\mathbb{F}_{p}+\cdots+u^{m-1}\mathbb{F}_{p}$ be a finite non-chain ring, where $u^m=u$ and $p$ is a prime congruent to $1$ modulo $(m-1)$. In this…
We introduce a consistent and efficient method to construct self-dual codes over $GF(q)$ with symmetric generator matrices from a self-dual code over $GF(q)$ of smaller length where $q \equiv 1 \pmod 4$. Using this method, we improve the…
In this paper we study a special type of quasi-cyclic (QC) codes called skew QC codes. This set of codes is constructed using a non-commutative ring called the skew polynomial rings $F[x;\theta ]$. After a brief description of the skew…