Related papers: On Cyclic DNA Codes

Let $\mathbb{F}_{p^m}$ be a finite field of cardinality $p^m$ and $R=\mathbb{F}_{p^m}[u]/\langle u^2\rangle=\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$ $(u^2=0)$, where $p$ is an odd prime and $m$ is a positive integer. For any $\alpha,\beta\in…

Cyclic codes are an interesting type of linear codes and have applications in communication and storage systems due to their efficient encoding and decoding algorithms. They have been studied for decades and a lot of progress has been made.…

A class of one-dimensional convolutional codes will be presented. They are all MDS codes, i. e., have the largest distance among all one-dimensional codes of the same length n and overall constraint length delta. Furthermore, their extended…

We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalizes the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and…

Double-stranded DNA `overstretches' at a pulling force of about 65 pN, increasing in length by a factor of 1.7. The nature of the overstretched state is unknown, despite its considerable importance for DNA's biological function and…

Let $\mathbb{F}_{q}$ be a finite field of cardinality $q$, $R=\mathbb{F}_{q}[u]/\langle u^4\rangle=\mathbb{F}_{q}+u\mathbb{F}_{q}+u^2\mathbb{F}_{q}+u^3\mathbb{F}_{q}$ $(u^4=0)$ which is a finite chain ring, and $n$ be a positive integer…

In this paper we investigate the structure of repeated root constacyclic codes of length $2^amp^r$ over $\mathbb{F}_{p^s}$ with $a\geq1$ and $(m,p)=1$. We characterize the codes in terms of their generator polynomials. This provides simple…

We study quasi-cyclic codes of index 2 over finite fields. We give a classification of such codes. Their duals with respect to the Euclidean, symplectic and Hermitian inner products are investigated. We describe self-orthogonal and…

The main objective of this paper is to extend the previously defined code family over the ring $\mathfrak{R}=\sum\limits_{s=0}^{4} v_{5}^{s} \mathcal{A}_{4}$ to $\mathfrak{R}^{s,m}=\sum\limits_{\varsigma=1}^{m}…

It is known that, for transmission over quasi-static MIMO fading channels with n transmit antennas, diversity can be obtained by using an inner fully diverse space-time block code while coding gain, derived from the determinant criterion,…

The results of J. F. Qiann et al. [4] on $(1-\gamma)$-cyclic codes over finite chain rings of nilpotency index 2 are extended to $(1-\gamma^e)$-cyclic codes over finite chain rings of arbitrary nilpotency index $e+1$. The Gray map is…

Let $\mathbb{F}_{2^m}$ be a finite field of $2^m$ elements, and $R=\mathbb{F}_{2^m}[u]/\langle u^k\rangle=\mathbb{F}_{2^m}+u\mathbb{F}_{2^m}+\ldots+u^{k-1}\mathbb{F}_{2^m}$ ($u^k=0$) where $k$ is an integer satisfying $k\geq 2$. For any odd…

The distance profiles of linear block codes can be employed to design variational coding scheme for encoding message with variational length and getting lower decoding error probability by large minimum Hamming distance. %, e.g. the design…

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…

A locally recoverable code of locality $r$ over $\mathbb{F}_{q}$ is a code where every coordinate of a codeword can be recovered using the values of at most $r$ other coordinates of that codeword. Locally recoverable codes are efficient at…

DNA sequences are prone to creating secondary structures by folding back on themselves by non-specific hybridization among its nucleotides. The formation of secondary structures makes the sequences chemically inactive towards synthesis and…

Two-dimensional cyclic codes of length $n=\ell s$ over the finite field $\mathbb{F}$ are ideals of the polynomial ring $\frac{\mathbb{F}[x,y]}{< x^{s}-1,y^{\ell}-1 >}$. The aim of this paper, is to present a novel method to study the…

Cyclic codes are an interesting family of linear codes since they have efficient decoding algorithms and contain optimal codes as subfamilies. Constructing infinite families of cyclic codes with good parameters is important in both theory…

Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Cyclic codes have been studied for many years, but their weight…

We study additive quaternary codes whose parameters are close to those of the extended cyclic [12; 6; 6]4-code or to the quaternary linear codes generated by the elliptic quadric in PG(3; 4) or its dual. In particular we characterize those…