Geodesic
Code loops in both parities
Journal of Algebraic Combinatorics, Tome 31 (2010) no. 4, pp. 585-611.

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Summary: We present equivalent definitions of code loops in any characteristic $p\neq 0$. 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: 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 
@article{JAC_2010__31_4_a0,
     author = {Dr\'apal, Ale\v{s} and Vojt\v{e}chovsk\'y, Petr},
     title = {Code loops in both parities},
     journal = {Journal of Algebraic Combinatorics},
     pages = {585--611},
     publisher = {mathdoc},
     volume = {31},
     number = {4},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2010__31_4_a0/}
}
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Drápal, Aleš; Vojtěchovský, Petr. Code loops in both parities. Journal of Algebraic Combinatorics, Tome 31 (2010) no. 4, pp. 585-611. http://geodesic.mathdoc.fr/item/JAC_2010__31_4_a0/