Corrigendum Parallelisms of P G(3, 4) with Automorphisms of Order 5
نویسندگان
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. A parallelism is transitive if it has an automorphism group which is transitive on the spreads. A parallelism is point-transitive if it has an automorphism group which is transitive on the points. If the automorphism group fixes one spread and is transitive on the remaining spreads, the parallelism corresponds to a transitive deficiency one partial parallelism. In PG(3, 4) there are no transitive parallelisms. No examples of point-transitive and no examples of transitive deficiency one parallelisms of PG(3, 4) are known. We construct all 28270 nonisomorphic parallelisms with automorphisms of order 5. None of them is point-transitive. There are 28100 ones with an automorphism group fixing exactly one spread, but none of them is transitive on the remaining spreads. We conclude that there are no point-transitive parallelisms and no transitive deficiency one parallelisms in PG(3, 4).
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