Related papers: Two generalizations on the minimum Hamming distanc…
We derive theoretical upper and lower bounds on the maximum size of DNA codes of length n with constant GC-content w and minimum Hamming distance d, both with and without the additional constraint that the minimum Hamming distance between…
A new lower bound on the minimum Hamming distance of linear quasi-cyclic codes over finite fields is proposed. It is based on spectral analysis and generalizes the Semenov- Trifonov bound in a similar way as the Hartmann-Tzeng bound extends…
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…
In this paper we investigate the class of constacyclic codes, which is a natural generalization of the class of cyclic and negacyclic codes. This class of codes is interesting in the sense that it contains codes with good or even optimal…
In this paper, we determine depth spectra of all repeated-root $(\alpha+\gamma \beta)$-constacyclic codes of arbitrary lengths over a finite commutative chain ring $\mathcal{R},$ where $\alpha$ is a non-zero element of the Teichm\"{u}ller…
Let $p$ be a prime number and $\varsigma$ and $m$ be a positive integers. Let $\mathcal{R} = \mathbb{F}_{2^m} + u\mathbb{F}_{2^m} + u^2\mathbb{F}_{2^m}$ ($u^3 = 0$). Cyclic codes of length $2^\varsigma$ over $\mathcal{R}$ are precisely the…
We consider two-dimensional $(\lambda_1, \lambda_2)$-constacyclic codes over $\mathbb{F}_{q}$ of area $M N$, where $q$ is some power of prime $p$ with $\gcd(M,p)=1$ and $\gcd(N,p)=1$. With the help of common zero (CZ) set, we characterize…
In this paper, a unique form of generators of a constacyclic code of arbitrary length over a non-chain ring of the type $\mathtt{R_{_{\theta}}}=Z_{4}+\nu Z_{4}, \nu^{2}=\theta \in Z_{4}+\nu Z_{4}$ has been obtained. Further, rank and…
Let $\mathbb{F}_p$ be a finite field and $u$ be an indeterminate. This article studies $(1-2u^k)$-constacyclic codes over the ring $\mathcal{R}=\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_p+u^{3}\mathbb{F}_{p}+\cdots+u^{k}\mathbb{F}_{p}$ where…
The use of skew polynomial rings allows to endow linear codes with cyclic structures which are not cyclic in the classical (commutative) sense. Whenever these skew cyclic structures are carefully chosen, some control over the Hamming…
The generalized Hamming weight (GHW) $d_r(C)$ of linear codes $C$ is a natural generalization of the minimum Hamming distance $d(C)(=d_1(C))$ and has become one of important research objects in coding theory since Wei's originary work [23]…
It is shown that subclasses of separable binary Goppa codes, $\Gamma(L,G)$ - codes, with $L=\{\alpha \in GF(2^{2l}):G(\alpha)\neq 0 \}$ and special Goppa polynomials G(x) can be presented as a chain of embedded codes. The true minimal…
Recently, a new algorithm to test equivalence of two cyclic codes has been introduced which is efficient and produced useful results. In this work, we generalize this algorithm to constacyclic codes. As an application of the algorithm we…
In this article we investigate Berlekamp's negacyclic codes and discover that these codes, when considered over the integers modulo 4, do not suffer any of the restrictions on the minimum distance observed in Berlekamp's original papers.…
Let $\mathbb{F}_{p^{m}}$ be a finite field with cardinality $p^{m}$ and $R=\mathbb{F}_{p^{m}}+u\mathbb{F}_{p^{m}}$ with $u^{2}=0$. We aim to determine all $\alpha+u\beta$-constacyclic codes of length $np^{s}$ over $R$, where…
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 =…
Let $\mathbb{F}_p$ be a finite field and $u$ be an indeterminate. This article studies $(1-2u^2)$-constacyclic codes over the ring $\mathbb{F}_p+u\mathbb{F}_p+u^2\mathbb{F}_p$, where $u^3=u$. We describe generator polynomials of this kind…
Symbol-pair codes introduced by Cassuto and Blaum (2010) are designed to protect against pair errors in symbol-pair read channels. The higher the minimum pair distance, the more pair errors the code can correct. MDS symbol-pair codes are…
The construction of self-dual codes over small fields such that their minimum distances are as large as possible is a long-standing challenging problem in the coding theory. In 2009, a family of binary self-dual cyclic codes with lengths…
Multi-dimensional cyclic code is a natural generalization of cyclic code. In an earlier paper we explored two-dimensional constacyclic codes over finite fields. Following the same technique, here we characterize the algebraic structure of…