A matrix based list decoding algorithm for linear codes over integer residue rings.

In this paper we address the problem of list decoding of linear codes over an integer residue ring Z q , where q is a power of a prime p. The proposed procedure exploits a particular matrix representation of the linear code over Z p r , called the standard form, and the p -adic expansion of the to-be-decoded vector. In particular, we focus on the erasure channel in which the location of the errors is known. This problem then boils down to solving a system of linear equations with coefficients in Z p r . From the parity-check matrix representations of the code we recursively select certain equations that a codeword must satisfy and have coefficients only in the field p r − 1 Z p r . This yields a step by step procedure obtaining a list of the closest codewords to a given received vector with some of its coordinates erased. We show that such an algorithm actually computes all possible erased coordinates, that is, the provided list is minimal. [ABSTRACT FROM AUTHOR]