Research ArticleNo Access

On the cycle index and the weight enumerator II

Himadri Shekhar Chakraborty

Graduate School of Natural Science and Technology, Kanazawa University, Ishikawa 920-1192, Japan

Department of Mathematics, Shahjalal University of Science and Technology, Sylhet-3114, Bangladesh

E-mail Address: himadri-mat@sust.edu

Corresponding author.

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Tsuyoshi Miezaki

Faculty of Science and Engineering, Waseda University, Tokyo 169–8555, Japan

E-mail Address: miezaki@waseda.jp

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, and

Manabu Oura

Faculty of Mathematics and Physics, Kanazawa University, Ishikawa 920–1192, Japan

E-mail Address: oura@se.kanazawa-u.ac.jp

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https://doi.org/10.1142/S0219498824502359Cited by:0 (Source: Crossref)

Abstract

In a previous paper, the second and third named authors introduced the concept of the complete cycle index and discussed a relation with the complete weight enumerator in coding theory. In this paper, we introduce the concept of the complete joint cycle index and the average complete joint cycle index, and discuss a relation with the complete joint weight enumerator and the average complete joint weight enumerator, respectively, in coding theory. Moreover, the notion of the average intersection numbers is given, and we discuss a relation with the average intersection numbers in coding theory.

Communicated by André Leroy

Keywords:

AMSC: 11T71, 20B05, 11H71

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