An Upper Bound of the Number of Covering Polynomials for a Class of Cyclic Codes and the Method to Find the Covering Polynomials

Yu Kangyou

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An Upper Bound of the Number of Covering Polynomials for a Class of Cyclic Codes and the Method to Find the Covering Polynomials

更新时间：2025-12-08

- An Upper Bound of the Number of Covering Polynomials for a Class of Cyclic Codes and the Method to Find the Covering Polynomials
- Acta Electronica Sinica Issue 4, Pages: 25-31(1992)
- 作者机构：
  
  1.   中国电子设备系统工程公司研究所五室
  2.   齐齐哈尔第一机床厂设计处北京 100039
  3.   齐齐哈尔 161005
- 作者简介：
- 基金信息：
- DOI：
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- Published：1992
- 稿件说明：
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[1]于康友,李良.一类循环码覆盖多项式个数的上界及其覆盖多项式的求取方法[J].电子学报,1992(04):25-31.

Yu Kangyou. An Upper Bound of the Number of Covering Polynomials for a Class of Cyclic Codes and the Method to Find the Covering Polynomials[J]. Acta Electronica Sinica, 1992, (4): 25-31.
[1]于康友,李良.一类循环码覆盖多项式个数的上界及其覆盖多项式的求取方法[J].电子学报,1992(04):25-31. DOI：

Yu Kangyou. An Upper Bound of the Number of Covering Polynomials for a Class of Cyclic Codes and the Method to Find the Covering Polynomials[J]. Acta Electronica Sinica, 1992, (4): 25-31. DOI：

摘要

Tadao Kasami提出了一种循环码的覆盖多项式译码法

该方法实现简单

速度也较快。但是

该方法的关键是寻求循环码的一个覆盖多项式集合。给定一个循环码

求取它的覆盖多项式集合目前尚无系统的方法。本文首先对循环码进行了分类

而后对Ⅱ-型循环码覆盖多项式的个数给出了一个上界

并且给出了一种具体求取Ⅱ-型循环码的覆盖多项式集合的一种方法。

Abstract

Tadao Kasami[1] proposed a decoding method for cyclic codes. This method has higher speed and simple construction. The key point of this method is to find a set of covering polynomials. For a cyclic code

it is difficult to find the set of it’s covering polynomials. We have not had a systematic method to find it. In this paper

we first classify the cyclic codes

then give a upper hound of the number of covering polynomials

and a method to find the set of the covering polynomials for the Ⅱ-type cyclic codes.

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