Divisibility properties for covering radius of certain cyclic codes

Moreno O.; Castro F.N.

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Divisibility properties for covering radius of certain cyclic codes

机译：覆盖某些循环码半径的可除性

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摘要

We are presenting a new method to obtain the covering radius of codes and in particular to prove quasi-perfection in codes. Our techniques combine divisibility results of Ax-Katz and Moreno-Moreno as well as coding theoretic methods. We answer a problem posed by Cohen-Honkala-Litsyn-Lobstein in the book covering radius for Bose-Chaudhuri-Hocquenghem (BCH) codes. We also obtain the covering radius for many new classes of codes.

机译：我们提出了一种新的方法来获得代码的覆盖半径，特别是证明代码的准完美。我们的技术结合了Ax-Katz和Moreno-Moreno的可除性结果以及编码理论方法。我们回答了Cohen-Honkala-Litsyn-Lobstein在书中所涉及的Bose-Chaudhuri-Hocquenghem（BCH）代码半径问题。我们还获得了许多新型代码的覆盖半径。

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来源
《IEEE Transactions on Information Theory》 |2003年第12期|p.3299-3303|共5页
作者
Moreno O.; Castro F.N.;
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作者单位

Dept. of Math. & Comput. Sci., Puerto Rico Univ., Rio Piedras, Puerto Rico;

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原文格式 PDF
正文语种 eng
中图分类无线电电子学、电信技术;
关键词
BCH codes; cyclic codes; polynomials; Galois fields; divisibility properties; code covering radius; cyclic codes; BCH code; finite fields; quasiperfect code; polynomial equation;

机译：BCH代码;循环代码;多项式;Galois字段;可分性;代码覆盖半径;循环代码;BCH代码;有限域;拟完美代码;多项式方程;

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专利

1. Correction to “Divisibility Properties for Covering Radius of Certain Cyclic Codes” [J] . Moreno O., Castro F.N., Mattson H.F. Jr. IEEE Transactions on Information Theory . 2006,第4期

机译：对“覆盖某些循环码半径的除数属性”的更正
2. ON THE COVERING RADIUS OF SOME BINARY CYCLIC CODES [J] . Arce-Nazario Rafael, Castro Francis N., Ortiz-Ubarri Jose Advances in mathematics of communications . 2017,第2期

机译：关于一些二进制循环码的覆盖半径
3. Linear codes with covering radius 2 and other new covering codes [J] . Gabidulin E.M., Davydov A.A. IEEE Transactions on Information Theory . 1991,第1期

机译：覆盖半径为2的线性代码和其他新的覆盖代码
4. Divisibility properties for covering radius of certain cyclic codes [C] . Oscar Moreno, Francis N. Castro IEEE International Symposium on Information Theory . 2002

机译：用于覆盖某些循环码的半径的可分性性质
5. On divisible codes over finite fields [D] . Liu, Xiaoyu 2006

机译：关于有限域上的可除码
6. New nonbinary code bounds based on divisibility arguments [O] . Sven C. Polak -1

机译：基于除数参数的新的非二进制代码范围
7. On the covering radius of cyclic linear codes and arithmetic codes [O] . Helleseth Tor 1985

机译：关于循环线性码和算术码的覆盖半径

Divisibility properties for covering radius of certain cyclic codes

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