Counting Extended Irreducible Goppa Codes
Kondwani Magamba, John A. Ryan

TL;DR
This paper establishes an upper bound on the number of extended irreducible Goppa codes over finite fields, contributing to the understanding of their combinatorial properties and potential applications in coding theory.
Contribution
It provides a new upper bound for the count of extended irreducible Goppa codes of specified degree and length, advancing theoretical knowledge in coding theory.
Findings
Derived an explicit upper bound for code count
Focused on codes with prime degree and length parameters
Enhances understanding of code enumeration in finite fields
Abstract
We obtain an upper bound on the number of extended irreducible q-ary Goppa codes of degree and length , where and and are prime numbers.
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