Enumeration of AGL(m/3, double struck capital Fp³)-invariant extended cyclic codes

• Authors: Xiang-Dong Hou
• Venue: International Journal of Information and Coding Theory
• Year: 2010

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 p^m over double struck capital F_{p^r which are invariant under the affine linear group AGL(m/e, double struck capital Fp^e)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 p^m over double struck capital Fp^r.}