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An alternative approach to the classification of the regular near hexagons with parameters (s,t,t(2)) = (2,11,1)

Bart De Bruyn (UGent)
(2015) ARS COMBINATORIA. 120. p.341-352
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Abstract
Based on some results of Shult and Yanushka [7], Brouwer [1] proved that there exists a unique regular near hexagon with parameters (s,t, t(2)) = (2, 11, 1), namely the one related to the extended ternary Golay code. His proof relies on the uniqueness of the Witt design S(5, 6,12), Pless's characterization of the extended ternary Golay code G(12) and some properties of S(5, 6,12) and G(12). It is possible to avoid all this machinery and to give an alternative more elementary and self-contained proof for the uniqueness. It was only observed recently by the author that such an alternative proof is implicit in the literature: it can be obtained by combining some results from the papers [1], [4] and [7]. This survey paper has the aim to bring this fact to the attention of the mathematical community. We describe the parts of the above papers which are relevant for this alternative proof of the classification. The alternative proof also requires that we prove a number of extra facts which are not explicitly contained in any of the three above papers. The present paper can also been seen as an addendum to Section 6.5 of the book [3] where the uniqueness of the near hexagon was not proved.
Keywords
Golay code, near hexagon, generalized quadrangle, POINTS

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Chicago
De Bruyn, Bart. 2015. “An Alternative Approach to the Classification of the Regular Near Hexagons with Parameters (s,t,t(2)) = (2,11,1).” Ars Combinatoria 120: 341–352.
APA
De Bruyn, B. (2015). An alternative approach to the classification of the regular near hexagons with parameters (s,t,t(2)) = (2,11,1). ARS COMBINATORIA, 120, 341–352.
Vancouver
1.
De Bruyn B. An alternative approach to the classification of the regular near hexagons with parameters (s,t,t(2)) = (2,11,1). ARS COMBINATORIA. 2015;120:341–52.
MLA
De Bruyn, Bart. “An Alternative Approach to the Classification of the Regular Near Hexagons with Parameters (s,t,t(2)) = (2,11,1).” ARS COMBINATORIA 120 (2015): 341–352. Print.
@article{7140146,
  abstract     = {Based on some results of Shult and Yanushka [7], Brouwer [1] proved that there exists a unique regular near hexagon with parameters (s,t, t(2)) = (2, 11, 1), namely the one related to the extended ternary Golay code. His proof relies on the uniqueness of the Witt design S(5, 6,12), Pless's characterization of the extended ternary Golay code G(12) and some properties of S(5, 6,12) and G(12). It is possible to avoid all this machinery and to give an alternative more elementary and self-contained proof for the uniqueness. It was only observed recently by the author that such an alternative proof is implicit in the literature: it can be obtained by combining some results from the papers [1], [4] and [7]. This survey paper has the aim to bring this fact to the attention of the mathematical community. We describe the parts of the above papers which are relevant for this alternative proof of the classification. The alternative proof also requires that we prove a number of extra facts which are not explicitly contained in any of the three above papers. The present paper can also been seen as an addendum to Section 6.5 of the book [3] where the uniqueness of the near hexagon was not proved.},
  author       = {De Bruyn, Bart},
  issn         = {0381-7032},
  journal      = {ARS COMBINATORIA},
  keyword      = {Golay code,near hexagon,generalized quadrangle,POINTS},
  language     = {eng},
  pages        = {341--352},
  title        = {An alternative approach to the classification of the regular near hexagons with parameters (s,t,t(2)) = (2,11,1)},
  volume       = {120},
  year         = {2015},
}

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