Combinatorial aspects of code loops

Petr Vojtěchovský

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 2, page 429-435
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Vojtěchovský, Petr. "Combinatorial aspects of code loops." Commentationes Mathematicae Universitatis Carolinae 41.2 (2000): 429-435. <http://eudml.org/doc/248622>.

@article{Vojtěchovský2000,
abstract = {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.},
author = {Vojtěchovský, Petr},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {code loops; symplectic cubic spaces; combinatorial polarization; binary linear codes; divisible codes; combinatorial polarization; binary linear code},
language = {eng},
number = {2},
pages = {429-435},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Combinatorial aspects of code loops},
url = {http://eudml.org/doc/248622},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Vojtěchovský, Petr
TI - Combinatorial aspects of code loops
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 2
SP - 429
EP - 435
AB - 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.
LA - eng
KW - code loops; symplectic cubic spaces; combinatorial polarization; binary linear codes; divisible codes; combinatorial polarization; binary linear code
UR - http://eudml.org/doc/248622
ER -

References

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  1. Aschbacher M., Sporadic Groups, Cambridge Tracts in Mathematics 104 (1994), Cambridge University Press. Zbl0804.20011MR1269103
  2. Chein O., Goodaire E., Moufang loops with a unique nonidentity commutator (associator, square), J. Algebra 130 (1990), 369-384. (1990) Zbl0695.20040MR1051308
  3. Griess R.L., Jr., Code loops, J. Algebra 100 (1986), 224-234. (1986) Zbl0589.20051MR0839580
  4. Hsu T., Moufang loops of class and cubic forms, Math. Proc. Camb. Phil. Soc., to appear. Zbl0962.20046MR1735310
  5. Vojtěchovský P., Derived Forms and Binary Linear Codes, Mathematics Report Number M99-10, Department of Mathematics, Iowa State University. 

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