An alternative construction of B-M and B-T unitals in desarguesian planes
نویسندگان
چکیده
We present a new construction of non-classical unitals from a classical unital U in PG(2, q2). The resulting non-classical unitals are B-M unitals. The idea is to find a non-standard model Π of PG(2, q2) with the following three properties: (i) points of Π are those of PG(2, q2); (ii) lines of Π are certain lines and conics of PG(2, q2); (iii) the points in U form a non-classical B-M unital in Π. Our construction also works for the B-T unital, provided that conics are replaced by certain algebraic curves of higher degree.
منابع مشابه
Constructions of unitals in Desarguesian planes
We present a new construction of non-classical unitals from a classical unital U in PG(2, q2). The resulting non-classical unitals are B–M unitals. The idea is to find a non-standard model Π of PG(2, q2) with the following three properties: (i) points of Π are those of PG(2, q2); (ii) lines of Π are certain lines and conics of PG(2, q2); (iii) the points in U form a non-classical B–M unital in ...
متن کاملEnumeration of Nonsingular Buekenhout Unitals
The only known enumeration of Buekenhout unitals occurs in the Desarguesian plane PG(2, q2). In this paper we develop general techniques for enumerating the nonsingular Buekenhout unitals embedded in any two-dimensional translation plane, and apply these techniques to obtain such an enumeration in the regular nearfield planes, the odd-order Hall planes, and the flag-transitive affine planes. We...
متن کاملPartial Unitals and Related Structures in Desarguesian Planes
It is shown that a partial unital with more than q √ q+1−√q points in the Desarguesian plane of order q can be extended to a unital.
متن کاملUnitals in Finite Desarguesian Planes
We show that a suitable 2-dimensional linear system of Hermitian curves of PG(2, q2) defines a model for the Desarguesian plane PG(2, q). Using this model we give the following group-theoretic characterization of the classical unitals. A unital in PG(2, q2) is classical if and only if it is fixed by a linear collineation group of order 6(q + 1)2 that fixes no point or line in PG(2, q2).
متن کاملAn upper bound for the minimum weight of the dual codes of desarguesian planes
We show that a construction described in Clark, Key and de Resmini [9] of small-weight words in the dual codes of finite translation planes can be extended so that it applies to projective and affine desarguesian planes of any order p where p is a prime, and m ≥ 1. This gives words of weight 2p + 1 − p −1 p−1 in the dual of the p-ary code of the desarguesian plane of order p, and provides an im...
متن کامل