Combinatorial aspects of code loops

Details Combinatorial aspects of code loops Combinatorial aspects of code loops

2007-01-24

arxiv.org/abs/math/0701691v1

proceedings of Loops '99, published in Comment. Math. Univ. Carolin. 41 (April 2000), no. 2, 429-435

Mathematics

Group Theory

6 pages

Scientific paper

The existence and uniqueness (up to equivalence) of code loops was first established by R. Griess. 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. Within this paper, we focus on their combinatorial construction and prove a more general result using the language of derived forms.

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