TY - JOUR

T1 - On the uniqueness of a certain thin near octagon (or partial 2-geometry, or parallelism) derived from the binary Golay code

AU - Brouwer, A.E.

PY - 1983

Y1 - 1983

N2 - The question of the uniqueness of a certain combinatorial structure has arisen in three contexts: a) is the regular near octagon with parameters(s,t_{2},t_{3},t)=(1, 1,2,23)unique [5]? b) is the partial2-geometry with nexus three and blocksize24unique [2]? c) is there a unique graph such that it is the graph of a parallelism ofleft(^{24}_{4}right)with respect to any [1]? We observe that these questions are equivalent and give an affirmative answer. In fact, we prove a more general theorem, showing the truth of a conjecture by Cameron.

AB - The question of the uniqueness of a certain combinatorial structure has arisen in three contexts: a) is the regular near octagon with parameters(s,t_{2},t_{3},t)=(1, 1,2,23)unique [5]? b) is the partial2-geometry with nexus three and blocksize24unique [2]? c) is there a unique graph such that it is the graph of a parallelism ofleft(^{24}_{4}right)with respect to any [1]? We observe that these questions are equivalent and give an affirmative answer. In fact, we prove a more general theorem, showing the truth of a conjecture by Cameron.

U2 - 10.1109/TIT.1983.1056664

DO - 10.1109/TIT.1983.1056664

M3 - Article

SN - 0018-9448

VL - 29

SP - 370

EP - 371

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 3

ER -