A Scheme of Error-detecting Codes

Acta Scientiarum Naturalium Universitatis Pekinensis

A Scheme of Error-detecting Codes

QIU Weisheng

Department of mathematics, School of Mathematical Sciences, Peking University, Beijing, 100871

Received:2000-03-17 Online:2001-01-20 Published:2001-01-20

一类检错编码方案

丘维声

北京大学数学科学学院数学系，北京，100871

Abstract

Abstract: It is presented that a scheme of error-detecting codes, give its computational methods, find probabilities detected of each type of error. In particular, a set of check character systems of 《National Standard of People's Republic of China: Data Processing-Check Character Systems》 and 《International Standard ISO 7064》can be derived from this scheme.

Key words: error-detecting codes, ring of congruence classes, probabilities detected of errors

摘要： 提出了一类检错编码方案，给出了它的计算方法，求出了它检查出各类错误的概率。特别地，从这类检错编码方案，可以推导出《中华人民共和国国家标准：数据处理——校验码系统》和《International Standard ISO 7064》中的各个校验码系统。

关键词: 检错编码, 剩余类环, 检错概率

CLC Number:

O157

QIU Weisheng. A Scheme of Error-detecting Codes[J]. Acta Scientiarum Naturalium Universitatis Pekinensis.

丘维声. 一类检错编码方案[J]. 北京大学学报（自然科学版）.

Add to citation manager EndNote|Ris|BibTeX

URL: https://xbna.pku.edu.cn/EN/

https://xbna.pku.edu.cn/EN/Y2001/V37/I1/1

[1]	WANG Shudong,YAN Lijun,LIU Xiangrong. On the Maximum Average Degree and the Incidence Chromatic Number [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2008, 44(5): 727-732.
[2]	WAN Zhaoze,LI Jian. Difference Sets in Groups of Order 4p⁴ [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2006, 42(5): 590-597.
[3]	CAO Xiwang,ZHU Yiquan,TANG Cui'e. A Note on Almost Perfect Arrays [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2005, 41(1): 15-20.
[4]	QIU Weisheng,CAI Kai. Construction and Enumeration for Periodic Quasi-Perfect Sequences and Multiplier Groups of Cyclic Hadamard Difference Sets of Type(II) [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2005, 41(1): 27-35.
[5]	CAO Xiwang. Some New Properties of Dickson Polynomials [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2004, 40(1): 12-18.
[6]	HAN Song,WANG Jie,GAO Li. New Provably Secure Signature Scheme [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2003, 39(5): 607-611.
[7]	LU Zaiping. On the Automorphism Groups of Bi-Cayley Graphs [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2003, 39(1): 1-5.
[8]	XIONG Guohua. Difference Sets with Classical Parameters and Bent Functions [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2003, 39(1): 14-16.
[9]	DENG Yingpu. On the p-Rank of Quadratic Residue Partial Difference Sets [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2003, 39(1): 17-21.
[10]	DENG Yingpu. A New Family of Divisible Difference Sets [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2002, 38(3): 312-314.
[11]	XIONG Guohua. A New Way of Constructing Hadamard Difference Sets [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2002, 38(3): 315-317.
[12]	WANG Zhangxiong. Orthogonal Bent Functions and High Nonlinearity Balanced Functions Satisfying SAC [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2002, 38(3): 318-322.
[13]	WAN Zhaoze. Difference Sets in Groups of Order 4p⁴ [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 2000, 36(3): 331-341.
[14]	WANG Zhangxiong. The Construction of a Class of Bent Sequences [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 1999, 35(3): 311-316.
[15]	WAN Zhaoze. A Note on Menon Difference Sets [J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 1999, 35(3): 281-284.