Related papers: On cyclic codes of length $2^e$ over finite fields
We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalize the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A.…
We address the problems of constructing quantum convolutional codes (QCCs) and of encoding them. The first construction is a CSS-type construction which allows us to find QCCs of rate 2/4. The second construction yields a quantum…
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 $\prod\limits_{i=1}^{n}\mathbb{Z}_{2^i}[x]/ \langle x^{\alpha_i}-1\rangle$; $\alpha_i$…
This paper is devoted to the units of integral group rings of cyclic $2$-groups of small orders, namely, the orders of $2^n$ for $n<8$. Immediately we should note the issues our consideration describe in the introduction in more detail.…
Linear intersection pairs of linear codes have become of interest due to their nice algebraic properties and wide applications. In this paper, we focus on linear intersection pairs of cyclic codes over finite fields. Some properties of…
Cyclic codes are among the most important families of codes in coding theory for both theoretical and practical reasons. Despite their prominence and intensive research on cyclic codes for over a half century, there are still open problems…
Two generalizations of the Hartmann--Tzeng (HT) bound on the minimum distance of q-ary cyclic codes are proposed. The first one is proven by embedding the given cyclic code into a cyclic product code. Furthermore, we show that unique…
Binary self-dual codes with large minimum distances, such as the extended Hamming code and the Golay code, are fascinating objects in the coding theory. They are closely related to sporadic simple groups, lattices and invariant theory. A…
We present a family of reducible cyclic codes constructed as the direct sum of two different semiprimitive two-weight irreducible cyclic codes. This family generalizes the class of reducible cyclic codes that was reported in the main result…
Let $R$ be a finite commutative chain ring with unique maximal ideal $\langle \gamma\rangle$, and let $n$ be a positive integer coprime with the characteristic of $R/\langle \gamma\rangle$. In this paper, the algebraic structure of cyclic…
We give the structure of $\lambda$-constacyclic codes of length $p^sm$ over $R=\mathbb{F}_{p^r}+u \mathbb{F}_{p^r}+...+ u^{e-1}\mathbb{F}_{p^r}$ with $\lambda \in \F_{p^r}^*$. We also give the structure of $\lambda$-constacyclic codes of…
In this study, in order to get better codes, we focus on double skew cyclic codes over the ring $\mathrm{R}= \mathbb{F}_q+v\mathbb{F}_q, ~v^2=v$ where $q$ is a prime power. We investigate the generator polynomials, minimal spanning sets,…
In this paper, we study skew cyclic codes with arbitrary length over the ring $R=\mathbb{F}_{p}+u\mathbb{F}_{p}$ where $p$ is an odd prime and $% u^{2}=0$. We characterize all skew cyclic codes of length $n$ as left $% R[x;\theta…
Let $\mathbb{F}_q$ be a finite field of order $q$, a prime power integer such that $q=et+1$ where $t\geq 1,e\geq 2$ are integers. In this paper, we study cyclic codes of length $n$ over a non-chain ring $R_{e,q}=\mathbb{F}_q[u]/\langle…
Due to the wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an interesting research topic in coding theory. In this paper, let $p$ be a prime with $p\ge 7$. We determine the…
New properties of $q$-ary cyclotomic cosets modulo $n = q^{m} - 1$, where $q \geq 3$ is a prime power, are investigated in this paper. Based on these properties, the dimension as well as bounds for the designed distance of some families of…
In this paper, we study cyclic codes over the ring $ \Z_p + u\Z_p +...+ u^{k-1}\Z_p $, where $u^k =0$. We find a set of generator for these codes. We also study the rank, the dual and the Hamming distance of these codes.
Let $p$ be a prime number. Irreducible cyclic codes of length $p^2-1$ and dimension $2$ over the integers modulo $p^h$ are shown to have exactly two nonzero Hamming weights. The construction uses the Galois ring of characteristic $p^h$ and…
In this paper, we describe linear and cyclic codes over the rings of the form $R_{s,p}=\mathbb{Z}_{p}[u]/\left( f\left(u\right) /\left( u-s\right) \right)$, where $p$ is a prime number and $f\left( u\right) =u^{p}-u$, with $s\in…
Subspace codes have received an increasing interest recently due to their application in error-correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and…