The Automorphism Groups of BCH Codes and of Some Affine-InvariantCodes Over Extension Fields

Authors:
Thierry P. Berger;Pascale Charpin
Affiliations:
UFR des Sciences de Limoges, 123 av. A. Thomas, 87060 Limoges Cedex, France;INRIA, Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France
Venue:
Designs, Codes and Cryptography
Year:
1999

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Abstract

Affine-invariant codesare extended cyclic codes of length p^m invariantunder the affine-group acting on {\F}_{p^m}. Thisclass of codes includes codes of great interest such as extendednarrow-sense BCH codes. In recent papers, we classified the automorphismgroups of affine-invariant codes berg, bech1. We derive herenew results, especially when the alphabet field is an extensionfield, by expanding our previous tools. In particular we completeour results on BCH codes, giving the automorphism groups of extendednarrow-sense BCH codes defined over any extension field.