### Journals Information

Mathematics and Statistics Vol. 9(5), pp. 648 - 652
DOI: 10.13189/ms.2021.090504
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## On the Representation of the Weight Enumerator of

Mans L Mananohas *, Charles E Mongi , Dolfie Pandara , Chriestie E J C Montolalu , Muhammad P M Mo'o
Department of Mathematics, Sam Ratulangi University, Indonesia

ABSTRACT

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.

KEYWORDS
Weight Enumator, Polynomial Ring, Isobaric Enumator

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Mans L Mananohas , Charles E Mongi , Dolfie Pandara , Chriestie E J C Montolalu , Muhammad P M Mo'o , "On the Representation of the Weight Enumerator of ," Mathematics and Statistics, Vol. 9, No. 5, pp. 648 - 652, 2021. DOI: 10.13189/ms.2021.090504.

(b). APA Format:
Mans L Mananohas , Charles E Mongi , Dolfie Pandara , Chriestie E J C Montolalu , Muhammad P M Mo'o (2021). On the Representation of the Weight Enumerator of . Mathematics and Statistics, 9(5), 648 - 652. DOI: 10.13189/ms.2021.090504.