2012/03/08 by Nicola Durante, N. Durante, Durante, N. +3
Computer Science · Mathematics · #Advanced Algebra and Geometry #Coding theory and cryptography #Finite Group Theory Research #math.CO
paper · pdf · doi:10.48550/arxiv.1203.1766
arxiv created 2012/03/08 · arxiv updated 2012/03/09
A unital in PG(2,q2) is a set U of q3+1 points such that each line meets U in 1 or q+1 points. The well known example is the classical unital consisting of all absolute points of a non-degenerate unitary polarity of PG(2,q2). Unitals other than the classical one also exist in PG(2,q2) for every q>2. Actually, all known unitals are of Buekenhout-Metz type and they can be obtained by a construction due to Buekenhout. The unitals constructed by Baker-Ebert, and independently by Hirschfeld-Szonyi, are the union of q conics. Our Theorem 1.1 shows that this geometric property characterizes the Baker-Ebert-Hirschfeld-Szonyi unitals.