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Title: Combinatorial aspects of code loops (English)
Author: Vojtěchovský, Petr
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 41
Issue: 2
Year: 2000
Pages: 429-435
Category: math
Summary: 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. (English)
Keyword: code loops
Keyword: symplectic cubic spaces
Keyword: combinatorial polarization
Keyword: binary linear codes
Keyword: divisible codes
MSC: 05A19
MSC: 20N05
MSC: 94B05
idZBL: Zbl 1042.94023
idMR: MR1780884
Date available: 2009-01-08T19:03:14Z
Last updated: 2012-04-30
Stable URL:
Reference: [1] Aschbacher M.: Sporadic Groups.Cambridge Tracts in Mathematics 104 (1994), Cambridge University Press. Zbl 0804.20011, MR 1269103
Reference: [2] Chein O., Goodaire E.: Moufang loops with a unique nonidentity commutator (associator, square).J. Algebra 130 (1990), 369-384. Zbl 0695.20040, MR 1051308
Reference: [3] Griess R.L., Jr.: Code loops.J. Algebra 100 (1986), 224-234. Zbl 0589.20051, MR 0839580
Reference: [4] Hsu T.: Moufang loops of class $2$ and cubic forms.Math. Proc. Camb. Phil. Soc., to appear. Zbl 0962.20046, MR 1735310
Reference: [5] Vojtěchovský P.: Derived Forms and Binary Linear Codes.Mathematics Report Number M99-10, Department of Mathematics, Iowa State University.


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