Elementary 2-group character codes
In this correspondence we describe a class of codes over GF(q), Where q is a power of an odd prime. These codes are analogs of the binary Reed-Muller codes and share several features in common with them. We determine the minimum weight and properties of these codes. For a subclass of codes we find the weight distribution and prove that the minimum nomzero weight codewords give 1-designs.
reed-muller codes group character codes linear codes