The n-dimensional key equation and a decoding application

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)