Code loops in both parities

Authors:
Aleš Drápal;Petr Vojtĕchovský
Affiliations:
Department of Algebra, Charles University, Prague, Czech Republic 186 75;Department of Mathematics, University of Denver, Denver, USA 80208
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2010

Citing 2
Cited 0

Sphere-packings, lattices, and groups

Sphere-packings, lattices, and groups
The Moufang loops of order 64 and 81

Journal of Symbolic Computation

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Abstract

We present equivalent definitions of code loops in any characteristic p≠0. The most natural definition is via combinatorial polarization, but we also show how to realize code loops by linear codes and as a class of symplectic conjugacy closed loops. For p odd, it is possible to define code loops via characteristic trilinear forms. Related concepts are discussed.