Theta functions and symmetric weight enumerators for codes over imaginary quadratic fields

Abstract: In this paper we continue the study of codes over imaginary quadratic fields and their weight enumerators and theta functions. We present new examples of non-equivalent codes over rings of characteristic $p=2$ and $p=5$ which have the same theta functions. We also look at a generalization of codes over imaginary quadratic fields, providing examples of non-equivalent pairs with the same theta function for $p=3$ and $p=5$.