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Counting irreducible Goppa codes

Part of: Finite fields and commutative rings (number-theoretic aspects) Theory of error-correcting codes and error-detecting codes

Published online by Cambridge University Press:  09 April 2009

Patrick Fitzpatrick  and
John A. Ryan
Patrick Fitzpatrick
Affiliation:
Department of Mathematics, University College Cork, Ireland e-mail: fitzpat@ucc.ie
John A. Ryan
Affiliation:
Department of Mathematics, Mzuzu University, Malawi, e-mail: mzuzu_jar@oceanfree.net
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Abstract

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We consider ineducible Goppa codes of length qm over Fq defined by polynomials of degree r, where q = pt and p, m, r are distinct primes. The number of such codes, inequivalent under coordinate permutations and field automorphisms, is determined.

Keywords

classical Goppa codesermeration

MSC classification

Secondary: 94B60: Other types of codes 11T71: Algebraic coding theory; cryptography

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 3 , December 2001 , pp. 299 - 306
Copyright
Copyright © Australian Mathematical Society 2001

References

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