ADDITIVE POLYCYCLIC CODES OVER F₄ INDUCED BY BINARY VECTORS AND SOME OPTIMAL CODES

In this paper, we study the structure and properties of additive right and left polycyclic codes induced by a binary vector a in F-2(n). We find the generator polynomials and the cardinality of these codes. We also study different duals for these codes. In particular, we show that if C is a right polycyclic code induced by a vector a is an element of F-2(n), then the Hermitian dual of C is a sequential code induced by a. As an application of these codes, we present examples of additive right polycyclic codes over F-4 with more codewords than comparable optimal linear codes as well as optimal binary linear codes and optimal quantum codes obtained from additive right polycyclic codes over F-4.