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Related papers: On automorphism groups of binary cyclic codes

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In this article we study the automorphism groups of binary cyclic codes. In particular, we provide explicit constructions for codes whose automorphism groups can be described as (a) direct products of two symmetric groups or (b) iterated…

Combinatorics · Mathematics 2009-03-23 Rolf Bienert , Benjamin Klopsch

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, monomials and trinomials over…

Information Theory · Computer Science 2013-10-08 Cunsheng Ding , Zhengchun Zhou

In this paper we initiate the study of cyclic algebraic geometry codes. We give conditions to construct cyclic algebraic geometry codes in the context of algebraic function fields over a finite field by using their group of automorphisms.…

Algebraic Geometry · Mathematics 2021-06-17 Gustavo Cabaña , María Chara , Ricardo A. Podestá , Ricardo Toledano

The automorphism groups of various linear codes are extensively studied yielding insights into the respective code structure. This knowledge is used in, e.g., theoretical analysis and in improving decoding performance, motivating the…

Information Theory · Computer Science 2024-04-16 Jonathan Mandelbaum , Sisi Miao , Holger Jäkel , Laurent Schmalen

Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first…

Information Theory · Computer Science 2016-11-18 Cunsheng Ding

As a subclass of linear codes, cyclic codes have efficient encoding and decoding algorithms, so they are widely used in many areas such as consumer electronics, data storage systems and communication systems. In this paper, we give a…

Information Theory · Computer Science 2019-08-09 Yan Liu , Xiwang Cao

This work introduces a decoding strategy for binary self-dual codes possessing an automorphism of a specific type. The proposed algorithm is a hard decision iterative decoding scheme. The enclosed experiments show that the new decoding…

Information Theory · Computer Science 2021-06-22 Radinka Yorgova

In this paper, we study groups of automorphisms of algebraic systems over a set of $p$-adic integers with different sets of arithmetic and coordinate-wise logical operations and congruence relations modulo $p^k,$ $k\ge 1.$ The main result…

Number Theory · Mathematics 2018-06-01 Ekaterina Yurova Axelsson , Andrei Khrennikov

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.…

Information Theory · Computer Science 2011-11-15 Cunsheng Ding

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…

Information Theory · Computer Science 2015-04-14 Eli Ben-Sasson , Tuvi Etzion , Ariel Gabizon , Netanel Raviv

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, almost perfect nonlinear…

Information Theory · Computer Science 2012-06-22 Cunsheng Ding

We determine the permutation groups that arise as the automorphism groups of cyclic combinatorial objects. As special cases we classify the automorphism groups of cyclic codes. We also give the permutations by which two cyclic combinatorial…

Information Theory · Computer Science 2012-07-16 Kenza Guenda , T. Aaron Gulliver

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. Inspired by the recent work on binary cyclic codes published in…

Information Theory · Computer Science 2023-01-18 Hai Liu , Chengju Li , Cunsheng Ding

The purpose of this paper is to present the structure of the linear codes over a finite field with q elements that have a permutation automorphism of order m. These codes can be considered as generalized quasi-cyclic codes. Quasi-cyclic…

Information Theory · Computer Science 2024-02-05 Stefka Bouyuklieva

Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra F[x]/(x^n-1), where F is a finite field. If this automorphism itself has certain specific cyclicity properties one is lead to the class of…

Rings and Algebras · Mathematics 2007-07-16 Heide Gluesing-Luerssen , Wiland Schmale

Over the past years, Polar codes have arisen as a highly effective class of linear codes, equipped with a decoding algorithm of low computational complexity. This family of codes share a common algebraic formalism with the well-known…

Combinatorics · Mathematics 2024-06-17 Jicheng Ma , Guiying Yan

In this note, an intrinsic description of some families of linear codes with symmetries is given, showing that they can be described more generally as quasi group codes, that is, as linear codes allowing a group of permutation automorphisms…

Information Theory · Computer Science 2021-11-11 Martino Borello , Wolfgang Willems

Cyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer applications due to their efficient encoding and decoding algorithms. In…

Information Theory · Computer Science 2012-07-12 Cunsheng Ding

A binary linear code $C$ is a $\mathbb{Z}_2$-double cyclic code if the set of coordinates can be partitioned into two subsets such that any cyclic shift of the coordinates of both subsets leaves invariant the code. These codes can be…

Information Theory · Computer Science 2014-10-22 Joaquim Borges , Cristina Fernández-Córdoba , Roger Ten-Valls

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…

Information Theory · Computer Science 2024-01-05 Somphong Jitman
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