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