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On the key equation for n-dimensional cyclic codes. Applications to decoding

Abstract : We introduce the key equation of a multidimensional code. This equation exhibits the error-locator polynomial as product of univariate polynomials and the error-evaluator polynomial as a multivariate polynomial. Then we reinterpret these polynomials in a multidimensional linear recurring sequence context. In particular, using the concept of section, we reduce the solution of the decoding problem to a succession of application of the Berlekamp-Massey algorithm. However, it must be noted that multidimensional codes which are usefull for applications and which are decodable by our algorithm are left to be found.
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https://hal.inria.fr/inria-00074879
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 4:43:03 PM
Last modification on : Friday, May 25, 2018 - 12:02:03 PM
Long-term archiving on: : Tuesday, April 12, 2011 - 7:52:49 PM

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  • HAL Id : inria-00074879, version 1

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Hervé Chabanne, Graham H. Norton. On the key equation for n-dimensional cyclic codes. Applications to decoding. [Research Report] RR-1796, INRIA. 1992. ⟨inria-00074879⟩

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