International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 29, Pages 1533-1541
Combinatorial polarization, code loops, and codes of high level
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 , where is a finite field and
is a finite-dimensional
vector space over . 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.