The n-dimensional key equation and a decoding application

Author

Chabanne, Hervé ; Norton, Graham H.

Author_Institution

Inst. Nat. de Recherche en Inf. et Autom., Le Chesnay, France

Volume

40

Issue

1

fYear

1994

fDate

1/1/1994 12:00:00 AM

Firstpage

200

Lastpage

203

Abstract

The author introduce the n-dimensional key equation, which exhibits the error-locator polynomial of an n-dimensional cyclic code as a product of n univariate polynomials and the error-evaluator polynomial as an n-variable polynomial. They then reinterpret these polynomials in the context of linear recurring sequences. In particular, they reduce the decoding problem to successive application of the Berlekamp-Massey algorithm. With this new method, they are able to decode (up to half their minimum distance) many codes in a table of 2-D cyclic codes due to Jensen (1985)

Keywords

cyclic codes; decoding; error correction codes; polynomials; 2D cyclic codes; Berlekamp-Massey algorithm; decoding; decoding application; error correcting codes; error-evaluator polynomial; error-locator polynomial; linear recurring sequences; minimum distance; n-dimensional cyclic code; n-dimensional key equation; n-variable polynomial; univariate polynomials; Algebra; Character generation; Decoding; Equations; Error correction codes; Galois fields; Information theory; Polynomials;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.272482

Filename

272482