Additive polycyclic codes over 2 p F for any prime p

Abstract

One of the most significant task in algebraic coding theory is to determine the structure of new class of linear or nonlinear codes and to find codes having good parameters. In this study, for any prime p , we define additive polycyclic codes over 2 p F as a generalization of additive polycyclic codes over F4 studied in [5]. By making use of the polynomials over F p instead of 2 p F , we determine the algebraic structure of additive polycyclic codes over 2 p F and present their generators completely. We also find the cardinality for these codes. Moreover, under certain conditions, we show that the Euclidean duals of additive polycyclic codes over 2 p F are also additive polycyclic codes over 2 p F . Finally, we illustrate what we discuss in this study by offering some examples of additive polycyclic codes over F9 that contain codewords as three times the number of the codewords of the optimal linear codes with the same length and minimum distance.