Related papers: Quasi-Cyclic Codes
A code is said to be equidistant if the distance between any two distinct codewords of the code is the same. In this paper, we have studied equidistant single-orbit cyclic and quasi-cyclic subspace codes. The orbit code generated by a…
In a recent paper, Tang and Ding introduced a class of binary cyclic codes of rate close to one half with a designed lower bound on their minimum distance. The definition involves the base $2$ expansion of the integers in their defining…
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, the cyclic codes of length $n$, where $n$ is odd with certain restrictions, over a finite chain ring $R$, have been studied using the structure of group algebra approach. The primitive idempotents of $RG$ of a finite cyclic…
Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. So far, most of previous results obtained were for cyclic codes with no more than three zeros. Recently, \cite{Y-X-D12}…
A numerical semigroup is a subset of N containing 0, closed under addition and with finite complement in N. An important example of numerical semigroup is given by the Weierstrass semigroup at one point of a curve. In the theory of…
Model sets play a fundamental role in structure analysis of quasicrystals. The diffraction diagram of a quasicrystal admits as symmetry group a finite group G, and there is a G-cluster C (union of orbits of G) such that the quasicrystal can…
Bicyclic codes are a generalization of the one dimensional (1D) cyclic codes to two dimensions (2D). Similar to the 1D case, in some cases, 2D cyclic codes can also be constructed to guarantee a specified minimum distance. Many aspects of…
The aim of this work is a systematic investigation of the possible parameters of quasi-perfect (QP) binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes. First we give a list of…
In this paper we study the structure of $\theta$-cyclic codes over the ring $B_k$ including its connection to quasi-$\tilde{\theta}$-cyclic codes over finite field $\mathbb{F}_{p^r}$ and skew polynomial rings over $B_k.$ We also…
In this paper, we construct the first families of asymmetric quantum convolutional codes (AQCC)'s. These new AQCC's are constructed by means of the CSS-type construction applied to suitable families of classical convolutional codes, which…
An 'arithmetic circuit' is a labeled, acyclic directed graph specifying a sequence of arithmetic and logical operations to be performed on sets of natural numbers. Arithmetic circuits can also be viewed as the elements of the smallest…
The structure of multivariate semisimple codes over a finite chain ring $R$ is established using the structure of the residue field $\bar R$. Multivariate codes extend in a natural way the univariate cyclic and negacyclic codes and include…
A new approach to bound the minimum distance of $q$-ary cyclic codes is presented. The connection to the BCH and the Hartmann--Tzeng bound is formulated and it is shown that for several cases an improvement is achieved. We associate a…
We study the asymptotic behavior of double and four circulant codes, which are quasi-cyclic codes of index two and four respectively. Exact enumeration results are derived for these families of codes with the prescribed hull dimension.…
Cyclic codes, as a crucial subclass of linear codes, exhibit broad applications in communication systems, data storage systems, and consumer electronics, primarily attributed to their well-structured algebraic properties. Let $p$ denote an…
Could the theories with hidden variables be employed for creation of a quantum computer? A particular scheme of quasiclassical model quantum computer structure is describe.
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…
Recent work has shown that properly designed protograph-based LDPC codes may have minimum distance linearly increasing with block length. This notion rests on ensemble arguments over all possible expansions of the base protograph. When…
Batch codes serve as critical tools for load balancing in distributed storage systems. While numerous constructions exist for specific batch sizes t, current methodologies predominantly rely on code dimension parameters, limiting their…