Title: Enumeration of AGL(m/3, double struck capital F_p³)-invariant extended cyclic codes

Authors: Xiang-Dong Hou

Addresses: Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA

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 p^m over double struck capital F_p^r which are invariant under the affine linear group AGL(m/e, double struck capital F_p^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 F_p³)-invariant linear codes of length p^m over double struck capital F_p^r.

Keywords: affine-invariant code; affine linear groups; extended cyclic codes; partial order; simplicial cones; walk.

DOI: 10.1504/IJICOT.2010.032137

International Journal of Information and Coding Theory, 2010 Vol.1 No.2, pp.214 - 243

Published online: 10 Mar 2010 *

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