Results 21 to 30 of about 159,782 (296)

Rank equivalent and rank degenerate skew cyclic codes

, 2016
Two skew cyclic codes can be equivalent for the Hamming metric only if they have the same length, and only the zero code is degenerate. The situation is completely different for the rank metric, where lengths of codes correspond to the number of outgoing
Martínez-Peñas, Umberto
core   +1 more source

Double Cyclic Codes over \({\mathbb{F}_{q}+v\mathbb{F}_{q}}\)

Mathematics, 2020
In this paper, an algebraic structure of a type of double cyclic codes is investigated, which covers some existing codes as special cases. The paper presents generic results about the generating polynomials, minimal generating sets, matrices and dual ...
Tenghui Deng, Jing Yang
doaj   +1 more source

The Weight Distributions of Cyclic Codes and Elliptic Curves

, 2011
Cyclic codes with two zeros and their dual codes as a practically and theoretically interesting class of linear codes, have been studied for many years. However, the weight distributions of cyclic codes are difficult to determine.
Qi, Yanfeng, Tang, Chunming, Wang, Baocheng, Xu, Maozhi, Yang, Yixian   +4 more
core   +1 more source

p-Adic estimates of Hamming weights in Abelian codes over Galois rings [PDF]

, 2006
A generalization of McEliece's theorem on the p-adic valuation of Hamming weights of words in cyclic codes is proved in this paper by means of counting polynomial techniques introduced by Wilson along with a technique known as trace-averaging introduced ...
Katz, Daniel J.
core   +1 more source

Subspace Polynomials and Cyclic Subspace Codes

, 2015
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 decoding ...
Ben-Sasson, Eli, Etzion, Tuvi, Gabizon, Ariel, Raviv, Netanel   +3 more
core   +1 more source

A Family of Five-Weight Cyclic Codes and Their Weight Enumerators

, 2013
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.
Ding, Cunsheng, Luo, Jinquan, Zhang, Aixian, Zhou, Zhengchun   +3 more
core   +2 more sources

The q-ary image of some qm-ary cyclic codes: permutation group and soft-decision decoding [PDF]

, 2002
Using a particular construction of generator matrices of the q-ary image of qm-ary cyclic codes, it is proved that some of these codes are invariant under the action of particular permutation groups.
Delpeyroux, Emmanuelle, Lacan, Jérôme
core   +1 more source

On double cyclic codes over $ \mathbb{Z}_2+u\mathbb{Z}_2 $

AIMS Mathematics
In this paper, we introduced double cyclic codes over $ R^r\times R^s $, where $ R = \mathbb{Z}_{2}+u\mathbb{Z}_{2} = \{0, 1, u, 1+u\} $ is the ring with four elements and $ u^2 = 0 $.
Ismail Aydogdu
doaj   +1 more source

Algebraic Quantum Synchronizable Codes

, 2016
In this paper, we construct quantum synchronizable codes (QSCs) based on the sum and intersection of cyclic codes. Further, infinite families of QSCs are obtained from BCH and duadic codes. Moreover, we show that the work of Fujiwara~\cite{fujiwara1} can
Guenda, K., Gulliver, T. A., La Guardia, G. G.   +2 more
core   +1 more source

Self-Dual and Complementary Dual Abelian Codes over Galois Rings [PDF]

, 2019
Self-dual and complementary dual cyclic/abelian codes over finite fields form important classes of linear codes that have been extensively studied due to their rich algebraic structures and wide applications.
Jitman, Somphong, Ling, San
core   +3 more sources