Related papers: Reversible and Reversible Complement Cyclic codes …
In this paper, several families of irreducible constacyclic codes over finite fields and their duals are studied. The weight distributions of these irreducible constacyclic codes and the parameters of their duals are settled. Several…
In this paper skew constacyclic codes over finite non-chain ring R = F_q+uF_q+vF_q, where q= p^m, p is an odd prime and u^{2}=u, v^{2}=v, uv = vu = 0 are studied. We show that Gray image of a skew alpha-constacyclic cyclic code of length n…
Generalized quasi-cyclic (GQC) codes form a natural generalization of quasi-cyclic (QC) codes. They are viewed here as mixed alphabet codes over a family of ring alphabets. Decomposing these rings into local rings by the Chinese Remainder…
In this article, we study the skew cyclic codes over R_{k}=F_{p}+uF_{p}+\dots +u^{k-1}F_{p} of length n. We characterize the skew cyclic codes of length $n$ over R_{k} as free left R_{k}[x;\theta]-submodules of R_{k}[x;\theta]/\langle…
In this work codes with availability are constructed based on the cyclic \emph{locally repairable code} (LRC) construction by Tamo et al. and their extension to $(r,\rho)$-locality by Chen et al. The minimum distance of these codes is…
A linear code with parameters $[n, k, n-k+1]$ is called a maximum distance separable (MDS for short) code. A linear code with parameters $[n, k, n-k]$ is said to be almost maximum distance separable (AMDS for short). A linear code is said…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Let $m=2\ell+1$ for an integer $\ell\geq 1$…
Many kinds of codes which possess two cycle structures over two special finite commutative chain rings, such as ${\Bbb Z}_2{\Bbb Z}_4$-additive cyclic codes and quasi-cyclic codes of fractional index etc., were proved asymptotically good.…
We study the construction of quasi-cyclic self-dual codes, especially of binary cubic ones. We consider the binary quasi-cyclic codes of length 3\ell with the algebraic approach of [9]. In particular, we improve the previous results by…
The applications of additive codes mainly lie in quantum error correction and quantum computing. Due to their applications in quantum codes, additive codes have grown in importance. In addition to this, additive codes allow the…
In this paper, we investigate $\theta$-skew cyclic codes over the ring $R= \mathbb{F}_4 + v \mathbb{F}_4$, where $v^2=v$ and $\theta$ is a non-trivial automorphism over $\mathbb{F}_4 + v \mathbb{F}_4$. This allows us to describe DNA code…
We consider locally repairable codes over small fields and propose constructions of optimal cyclic and linear codes in terms of the dimension for a given distance and length. Four new constructions of optimal linear codes over small fields…
In this paper, we provide a polynomial characterization of linear complementary pairs of quasi-cyclic and quasi-twisted codes of index 2. We also give several examples of linear complementary pairs of quasi-cyclic and quasi-twisted codes…
This paper investigates the application of the theoretical algebraic notion of a separable ring extension, in the realm of cyclic convolutional codes or, more generally, ideal codes. We work under very mild conditions, that cover all…
A problem of reconstructing words from their subwords involves determining the minimum amount of information needed, such as multisets of scattered subwords of a specific length or the frequency of scattered subwords from a given set, in…
A tree ${\mathbb T} =\langle T\leq \rangle$ is reversible iff there is no order $\preccurlyeq \;\varsubsetneq \;\leq $ such that ${\mathbb T} \cong \langle T ,\preccurlyeq\rangle$. Using a characterization of reversibility via back and…
We show that there are good long binary generalized quasi-cyclic self-dual (either Type I or Type II) codes.
Let $p$ be a prime number. In this paper, we discuss the structures of cyclic codes over the ring $ \mathbb{F}_p[u, v] / \langle u^k, v^2, uv-vu\rangle$. We find a unique set of generators for these codes. We also study the rank and the…
We consider recursive decoding techniques for RM codes, their subcodes, and newly designed codes. For moderate lengths up to 512, we obtain near-optimum decoding with feasible complexity.
In this paper, we study convolutional codes with a specific cyclic structure. By definition, these codes are left ideals in a certain skew polynomial ring. Using that the skew polynomial ring is isomorphic to a matrix ring we can describe…