Decoding a class of Lee metric codes over a Galois ring
Eimear Byrne · IEEE Transactions on Information Theory · 2002
We investigate a class of Lee (1958) metric alternant codes with symbols in Z/sub pn/, establishing a lower bound on the minimum Lee distance where certain restrictions are placed on the code parameters. Corresponding to this bound, we have devised a decoding algorithm which is implemented over a finite field. The algorithm proceeds by finding a Grobner basis of the module M of solutions to a key equation. We obtain a necessary characterization of the solution module by solving iteratively a linear sequence over a Galois ring and show that the particular solution sought by the decoder is minimal in M. The required solution can then be found in an appropriate Grobner basis of M.