On the cycle index and the weight enumerator
Tsuyoshi Miezaki, Manabu Oura
TL;DR
This paper introduces the complete cycle index and explores its relationship with the complete weight enumerator in coding theory, inspired by polynomial aspects of codes, matroids, and permutation groups.
Contribution
It defines the complete cycle index and establishes its connection with the complete weight enumerator, advancing the algebraic understanding of coding structures.
Findings
Established a formal relation between cycle index and weight enumerator.
Provided new algebraic tools for analyzing codes and permutation groups.
Extended polynomial methods in coding theory.
Abstract
In this paper, we introduce the concept of the complete cycle index and discuss a relation with the complete weight enumerator in coding theory. This work was motivated by Cameron's lecture note "Polynomial aspects of codes, matroids and permutation groups."
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Error Correcting Code Techniques