Enumeration of AGL(m/3, double struck capital Fp³)-invariant extended cyclic codes Online publication date: Wed, 10-Mar-2010
by Xiang-Dong Hou
International Journal of Information and Coding Theory (IJICOT), Vol. 1, No. 2, 2010
Abstract: Let p be a prime and let r, e and m be positive integers such that r|e and e|m. The enumeration of linear codes of length pm over double struck capital Fpr which are invariant under the affine linear group AGL(m/e, double struck capital Fpe)is equivalent to the enumeration of certain ideals in a partially ordered set (U, <) where U = {0, 1, ... , m/e(p−1)}e and < is defined by an e-dimensional simplicial cone. When e = 2, the enumeration problem was solved in an earlier paper. In this paper, we consider the cases e = 3. We describe methods for enumerating all AGL(m/3, double struck capital Fp3)-invariant linear codes of length pm over double struck capital Fpr.
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