On the cycle index and the weight enumerator II

TL;DR

This paper extends the concept of cycle indices in coding theory by introducing joint and average variants, exploring their relations with weight enumerators and intersection numbers.

Contribution

It introduces the complete joint cycle index and average complete joint cycle index, linking them to joint weight enumerators and intersection numbers in coding theory.

Findings

Defined the complete joint cycle index and average complete joint cycle index.

Established relations between these indices and joint weight enumerators.

Discussed the connection with average intersection numbers.

Abstract

In a previous paper, the second and third named author introduced the concept of the complete cycle index and discussed a relation with the complete weight enumerator in coding theory. In the present 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.