Geodesic
Combinatorial aspects of code loops
Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 2, pp. 429-435

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The existence and uniqueness (up to equivalence defined below) of code loops was first established by R. Griess in [3]. Nevertheless, the explicit construction of code loops remained open until T. Hsu introduced the notion of symplectic cubic spaces and their Frattini extensions, and pointed out how the construction of code loops followed from the (purely combinatorial) result of O. Chein and E. Goodaire contained in [2]. Within this paper, we focus on their combinatorial construction and prove a more general result 2.1 using the language of derived forms.
Classification : 05A19, 20N05, 94B05
Keywords: code loops; symplectic cubic spaces; combinatorial polarization; binary linear codes; divisible codes 
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Vojtěchovský, Petr. Combinatorial aspects of code loops. Commentationes Mathematicae Universitatis Carolinae, Tome 41 (2000) no. 2, pp. 429-435. http://geodesic.mathdoc.fr/item/CMUC_2000__41_2_a19/