International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 29, Pages 1533-1541

Combinatorial polarization, code loops, and codes of high level

Petr Vojtěchovský

Department of Mathematics, University of Denver, 2360 S. Gaylord Street, Denver 80208, CO, USA

Received 22 June 2003

Copyright © 2004 Petr Vojtěchovský. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We first find the combinatorial degree of any map f:VF, where F is a finite field and V is a finite-dimensional vector space over F. We then simplify and generalize a certain construction, due to Chein and Goodaire, that was used in characterizing code loops as finite Moufang loops that possess at most two squares. The construction yields binary codes of high divisibility level with prescribed Hamming weights of intersections of codewords.