Decoding a Class of Alternant Codes for the Lee Metric

We investigate a class of Lee-metric alternant codes with symbols in Zpn, 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 two decoding algorithms. The first operates entirely over a Galois ring, while the second must be implemented over the associated residue field. The algorithms proceed by finding a Grِbner basis of the module M of solutions to a key equation. We obtain a necessary characterisation 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. Hence the required solution can be found in an appropriate Grِbner basis of M.