Enumeration of AGL(m/3, F_(p~3))-invariant extended cyclic codes

摘要

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 F_(p~r) which are invariant under the affine linear group AGL(m|e, F_(p~e)) is equivalent to the enumeration of certain ideals in a partially ordered set (U, <) whereW = {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, F_(p~3) -invariant linear codes of length p~m over F_(p~r).