  Polycyclic codes are a generalization of cyclic and constacyclic codes. Even
though they have been known since 1972 and received some attention more
recently, there have not been many studies on polycyclic codes. This paper
presents an in-depth investigation of polycyclic codes associated with
trinomials. Our results include a number of facts about trinomials, some
properties of polycyclic codes, and many new quantum codes derived from
polycyclic codes. We also state several conjectures about polynomials and
polycyclic codes. Hence, we show useful features of polycyclic codes and
present some open problems related to them.
