On the classification of unitals on 28 points of low rank

Titelangaben

Tonchev, Vladimir ; Wassermann, Alfred:
On the classification of unitals on 28 points of low rank.
In: Applicable Algebra in Engineering, Communication and Computing. Bd. 33 (2022) . - S. 903-913.
ISSN 1432-0622
DOI: https://doi.org/10.1007/s00200-022-00541-y

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Abstract

The classification of unitals with parameters 2-(28, 4, 1) according to the 2-rank of their incidence matrices was initiated by McGuire, Tonchev and Ward, who proved that the 2-rank of any unital on 28 points is greater than or equal to 19, and up to isomorphism, there is a unique unital with 2-rank equal to 19. Jaffe and Tonchev investigated the next two 2-ranks, 20 and 21, and showed that there are no unitals on 28 points with 2-rank equal to 20, and there are exactly 4 isomorphism classes of unitals of rank 21. The subject of this paper is the classification of unitals having 2-rank 22, 23 and 24.