Duality for Modules and Applications to Decoding Linear Codes over Finite Commutative Rings

Syndrome decoding is a more efficient method of decoding linear codes over finite fields over a noisy channel [5]. Thus, in this paper we investigate the generalization of the syndrome decoding to linear codes over finite commutative rings. A first generalization was given in [1] via Pontryagin duality. In the same direction we give another generalization using linear functional-based duality. In general, linear functionalbased duality and character-based (or Pontryagin) duality are not equivalent (for more details see [8]). Syndrome decoding of linear codes over finite fields is based on the two following famous results in linear algebra [9] : C = C (1)