Affine Invariant and Cyclic Codes over p-adic Numbers and Finite Rings
Designs, Codes and Cryptography
The Automorphism Groups of BCH Codes and of Some Affine-InvariantCodes Over Extension Fields
Designs, Codes and Cryptography
Enumeration of certain affine invariant extended cyclic codes
Journal of Combinatorial Theory Series A
There Are Not Non-obvious Cyclic Affine-invariant Codes
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Generalized Reed---Muller codes over $${\mathbb{Z}_q}$$
Designs, Codes and Cryptography
Enumeration of AGL(m/3, double struck capital Fp³)-invariant extended cyclic codes
International Journal of Information and Coding Theory
Switching construction of planar functions on finite fields
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
Codes over p-adic Numbers and Finite Rings Invariant under the Full Affine Group
Finite Fields and Their Applications
On the permutation groups of cyclic codes
Journal of Algebraic Combinatorics: An International Journal
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The extended cyclic codes of length pm, p is a prime, which are invariant under the affine-group acting on Fpm, are called affine-invariant codes. Following results of Berger (1996, 1994), we present the formal expression of the permutation group of these codes. Afterwards we give several tools in order to determine effectively the group of a given code or of some infinite class of codes. We next prove, by studying some examples, that our tools are efficient. In the end, we give our main application, the permutation group of primitive BCH codes defined on any prime field