Number of information symbols in polynomial codes

Polynomial codes and their dual codes as introduced by Kasami, Lin, and Peterson have considerable algebraic and geometric structure. It has been shown that these codes contain many well-known classes of cyclic codes as subclasses, such as BCH codes, projective geometry codes (PG codes), Euclidean geometry codes (EG codes), and generalized Reed-Muller codes (GRM codes). In this paper, combinatorial expressions for the number of information symbols and parity-check symbols in polynomial codes are derived. The results are applied to two important subclasses of codes, the PG codes and EG codes.