Quasi-self-reciprocal polynomials and potentially large minimum distance BCH codes

We consider the problem of determining which irreducible polynomials with coefficients in a finite field are quasi-self-reciprocal. Our characterization of these polynomials is in terms of a set of positive integers, . has applications to certain BCH codes. This work determines those codes (as specified by , the length of the code, and not by ) whose minimum-distance lower bound doubles when the root one is added to the code generator.