Permutation equivalent maximal irreducible Goppa codes
Francesca Dalla Volta (Dipartimento di Matematica e applicazioni, Universita' di Milano Bicocca), Marta Giorgetti (Dipartimento di Fisica e, Matematica Universita' dell'Insubria, Como), Massimiliano Sala (Dipartimento, di Matematica Universita' di Trento)
TL;DR
This paper investigates the classification of maximal irreducible Goppa codes by their permutation equivalence using group theory, aiming to determine the number of distinct codes with given parameters.
Contribution
It introduces a group-theoretic approach to count permutation non-equivalent Goppa codes with fixed parameters, providing new insights into their classification.
Findings
Derived formulas for counting permutation non-equivalent codes
Identified the role of group actions in code equivalence
Enhanced understanding of Goppa code diversity
Abstract
We consider the problem of finding the number of permutation non-equivalent classical irreducible maximal Goppa codes having fixed parameters q, n and r from a group theory point of view.
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cooperative Communication and Network Coding