Additive double polycyclic codes over Fp2 and their applications to quantum codes

Abstract

In this paper, we introduce additive double polycyclic codes over F-p(2) for any prime p. We study their algebraic structures and determine generator polynomials of these codes. We also give cardinality of them. Additionally, we establish that both Euclidean dual and Hermitian dual of an additive double polycyclic code over F-p(2) are also an additive double polycyclic code over F-p(2). As practical applications of these codes, we exhibit additive double polycyclic codes over F-9 which contain triple as many codewords as optimal linear codes of same length and minimum distance over F-9, and we derive optimal ternary linear codes and quantum codes from additive double polycyclic codes over (F)9.