Journal of Algebraic Combinatorics

, Volume 31, Issue 4, pp 585–611 | Cite as

Code loops in both parities

Article

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.

Keywords

Code loop Even code loop Odd code loop Symplectic loop Small Frattini loop Moufang loop Conjugacy closed loop Combinatorial polarization Symmetric associator Characteristic form Doubly even code Self-orthogonal code Kronecker product 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of AlgebraCharles UniversityPragueCzech Republic
  2. 2.Department of MathematicsUniversity of DenverDenverUSA

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