On the Representation of the Weight Enumerator of
Mans Mananohas, Charles E. Mongi, Dolfie Paulus Pandara, Chriestie E.J.C. Montolalu, Muhammad P M Moo · Mathematics and Statistics · 2021
The weight enumerator of a code is a homogeneous polynomial that provides a lot of information about the code. In this case, for the development of a code, research on the weight enumerator is very important. In this study, we focus on the code . Let be the weight enumerator of the code . Fujii and Oura showed that is generated by and . Indeed, we show that is an element of the polynomial ring . We know that the weight enumerator of all self-dual double-even (Type II) code is generated by and . Recall is a type II code. Thus, is an element of the polynomial ring and . One of the motivations of this research is to investigate the connection between these two polynomial rings in representing . Let and be the coefficients of polynomial that represent as an element of and , respectively. We find that is an element of the polynomial . In addition, we also show that there are no weight enumerators of Type II code generated by and that can be written uniquely as isobaric polynomials in five homogeneous polynomial elements of degrees 8, 24, 24, 24, 24.