Redundancy of Linear Codes based on Finite Rings

For linear codes based on finite fields, the Gilbert-Varshamov bound is a benchmark in measuring the efficiency in terms of the trade-off between overhead and error correction capability. In this paper we study redundancy of linear codes based on finite rings. We use the probabilistic method to obtain Gilbert-Varshamov type redundancy bounds for linear codes based on arbitrary finite rings and with a given relative distance.