Vectorial cyclic codes and their algebraic structures

Abstract

In Algebraic Coding Theory, constructing codes with optimal parameters, discoveringnew code families and subfamilies, proposing new algebraic coding methods,generalizing and applying these methods to various algebraic structures orconstructing best known codes in different and preferably more efficient ways haveall been important research subjects.In this study, polycyclic codes, which are based on polycyclic shift that createsvector-circulant matrices, are examined over different algebraic structures. The term"multi polycyclic codes" is contributed to the literature, with introducing generator andparity check conditions and duality theorems especially over skew polynomial rings.Moreover, a polycyclic code construction method is proposed over matrix spaces.