Parallelisms of PG ( 3 , 4 ) with automorphisms of order 3 Svetlana
نویسنده
چکیده
A spread is a set of lines of PG(d, q), which partition the point set. A parallelism is a partition of the set of lines by spreads. Some constructions of constant dimension codes that contain lifted MRD codes are based on parallelisms of projective spaces. It is known that there are 3 types of spreads in PG(3, 4) regular, subregular and aregular. A parallelism is regular if all its spreads are regular. There are no regular parallelisms in PG(3, 4). The maximum number of regular spreads which a parallelism of this projective space can have is not known. We construct all 8120217 nonisomorphic parallelisms with automorphisms of order 3 and classify them by the order of their automorphism group and by the type of their spreads. Among them there are examples of parallelisms with 13 regular spreads, which is the greatest number known by now.
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