相关论文: Repeated-root constacyclic codes over finite commu…
Let $q$ be a power of a prime $p$. In this paper, we study reversible cyclic codes of arbitrary length over the ring $ R = \mathbb{F}_q + u \mathbb{F}_q$, where $u^2=0 mod q$. First, we find a unique set of generators for cyclic codes over…
In an interesting paper Professor Cunsheng Ding provided three constructions of cyclic codes of length being a product of two primes. Numerical data shows that many codes from these constructions are best cyclic codes of the same length and…
Symbol-pair codes are block codes with symbol-pair metrics designed to protect against pair-errors that may occur in high-density data storage systems. MDS symbol-pair codes are optimal in the sense that it can attain the highest pair-error…
Let $r,s,t$ be three positive integers and $\mathcal{C}$ be a binary linear code of lenght $r+s+t$. We say that $\mathcal{C}$ is a triple cyclic code of lenght $(r,s,t)$ over $\mathbb{Z}_2$ if the set of coordinates can be partitioned into…
In this work, four circulant and quadratic double circulant (QDC) constructions are applied to the family of the rings R_k,m. Self-dual binary codes are obtained as the Gray images of self-dual QDC codes over R_k,m. Extremal binary…
In this paper, cyclic codes are established over some finite quaternion integer rings with respect to the quaternion Mannheim distance, and de- coding algorithm for these codes is given.
In this paper, we shall study k-Galois LCD constacyclic group codes over finite commutative chain rings with identity. In particular, we shall characterize Galois LCD constacyclic codes over finite commutative chain ring with identity in…
In this paper, we clarify some aspects on LCD codes in the literature. We first prove that a non-free LCD code does not exist over finite commutative Frobenius local rings. We then obtain a necessary and sufficient condition for the…
Let $\mathbb{F}_{p^m}$ be the field containing $p^m$ elements where $p$ is an odd prime and $m \in \mathbb{N}$. In this article, we propose a unified approach to the study of skew constacyclic codes of length $np^s$ over the ring $R_k =…
Polycyclic codes offer a natural generalization of cyclic codes and provide a broader algebraic framework for constructing linear codes with good parameters. In this paper, we study binary polycyclic codes associated with powers of…
We determine the asymptotic proportion of free modules over finite chain rings with good distance properties and treat the asymptotics in the code length n and the residue field size q separately. We then specialize and apply our technique…
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…
A class of linear block codes which simultaneously generalizes Gabidulin codes and a class of skew cyclic codes is defined. For these codes, both a Hartmann-Tzeng-like bound and a Roos-like bound, with respect to their rank distance, are…
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 method to construct and count all the linear codes (of arbitrary length) in $\mathbb{F}_{4}$ that are invariant under reverse permutation and that contain the repetition code is presented. These codes are suitable for constructing DNA…
We introduce a formula for determining the number of codewords of weight 2 in cyclic codes and provide results related to the count of codewords with weight 3. Additionally, we establish a recursive relationship for binary cyclic codes that…
Properties of matrix product codes over finite commutative Frobenius rings are investigated. The minimum distance of matrix product codes constructed with several types of matrices is bounded in different ways. The duals of matrix product…
Multiparameter persistence modules come up naturally in topological data analysis and topological robotics. Given a metric graph $(X,\delta)$, the second configuration space of $(X,\delta)$ with proximity parameters (for example, the…
Let $\mathbb{F}_{2^m}$ be a finite field of cardinality $2^m$, $R=\mathbb{F}_{2^m}[u]/\langle u^4\rangle)$ and $n$ is an odd positive integer. For any $\delta,\alpha\in \mathbb{F}_{2^m}^{\times}$, ideals of the ring $R[x]/\langle…
There is a local ring $E$ of order $4,$ without identity for the multiplication, defined by generators and relations as $E=\langle a,b \mid 2a=2b=0,\, a^2=a,\, b^2=b,\,ab=a,\, ba=b\rangle.$ We study a special construction of self-orthogonal…