Affine-invariant extended cyclic codes and partially ordered sets of antichains
Discrete Mathematics
On self-dual affine-invariant codes
Journal of Combinatorial Theory Series A
Sperner theory
Automorphism groups and permutation groups of affine-invariant codes
FFA '95 Proceedings of the third international conference on Finite fields and applications
The Automorphism Groups of BCH Codes and of Some Affine-InvariantCodes Over Extension Fields
Designs, Codes and Cryptography
The permutation group of affine-invariant extended cyclic codes
IEEE Transactions on Information Theory - Part 2
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
Enumeration of AGL(m/3, double struck capital Fp³)-invariant extended cyclic codes
International Journal of Information and Coding Theory
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Let p be a prime and let r, e, m be positive integers such that r|e and e|m. Extended cyclic codes of length pm over Fpr which are invariant under AGL(m/e, Fpe) are characterized by a well-known relation ℓe on the set {0, 1,...,pm - 1}. From the relation ℓe, we derive a partial order ≺ in u = {0, 1,...,m/e(p - 1)}e defined by an e-dimensional simplicial cone. We show that the aforementioned extended cyclic codes can be enumerated by the ideals of (u, ≺) which are invariant under the rth power of a circulant permutation matrix. When e = 2, we enumerate all such invariant ideals by describing their boundaries. Explicit formulas are obtained for the total number of AGL(m/2, Fp2)- invariant extended cyclic codes of length pm over Fpr and for the dimensions of such codes. We also enumerate all self-dual AGL(m/2, F22)-invariant extended cyclic codes of length 2m over F22 where m/2 is odd; the restrictions on the parameters are necessary conditions for the existence of self-dual affine invariant extended cyclic codes with e = 2.