Error-Locating Pairs for Cyclic Codes

Iwan M. Duursma; Ralf Kötter

doi:10.1109/18.335964

Error-Locating Pairs for Cyclic Codes

Iwan M. Duursma, Ralf Kötter

Research output: Contribution to journal › Article › peer-review

Abstract

A general decoding method for linear codes is investigated for cyclic codes. The decoding consists of solving two systems of linear equations. All but four binary cyclic codes of length less than 63 can so be decoded up to their actual distance. A new family of codes is given for which the decoding needs only O(n2) operations.

Original language	English (US)
Pages (from-to)	1108-1121
Number of pages	14
Journal	IEEE Transactions on Information Theory
Volume	40
Issue number	4
DOIs	https://doi.org/10.1109/18.335964
State	Published - Jul 1994
Externally published	Yes

Keywords

Algebraic decoding
MDS code
QR code
cyclic code
error-locating pair

ASJC Scopus subject areas

Information Systems
Computer Science Applications
Library and Information Sciences

Online availability

10.1109/18.335964

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title = "Error-Locating Pairs for Cyclic Codes",

abstract = "A general decoding method for linear codes is investigated for cyclic codes. The decoding consists of solving two systems of linear equations. All but four binary cyclic codes of length less than 63 can so be decoded up to their actual distance. A new family of codes is given for which the decoding needs only O(n2) operations.",

keywords = "Algebraic decoding, MDS code, QR code, cyclic code, error-locating pair",

author = "Duursma, {Iwan M.} and Ralf K{\"o}tter",

note = "Funding Information: Manuscript received March 22, 1993; revised October 21, 1993. The work of I. M. Duursma was supported by the Netherlands Organization for Scientific Research (WO), through the Stichting Mathematisch Centnun.",

year = "1994",

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AU - Kötter, Ralf

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PY - 1994/7

Y1 - 1994/7

N2 - A general decoding method for linear codes is investigated for cyclic codes. The decoding consists of solving two systems of linear equations. All but four binary cyclic codes of length less than 63 can so be decoded up to their actual distance. A new family of codes is given for which the decoding needs only O(n2) operations.

AB - A general decoding method for linear codes is investigated for cyclic codes. The decoding consists of solving two systems of linear equations. All but four binary cyclic codes of length less than 63 can so be decoded up to their actual distance. A new family of codes is given for which the decoding needs only O(n2) operations.

KW - Algebraic decoding

KW - MDS code

KW - QR code

KW - cyclic code

KW - error-locating pair

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ER -

Error-Locating Pairs for Cyclic Codes

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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