We show by a combination of theoretical argument and computer search that if a projective (75, 4, 12, 5) set in PG(3, 7) exists
then its automorphism group must be trivial. This corresponds to the smallest open case of a coding problem posed by H. Ward
in 1998, concerning the possible existence of an infinite family of projective two-weight codes meeting the Griesmer bound.
Mathematics Subject
... [Show full abstract] Classification (2010)05E20-05B25-94B05
KeywordsCentraliser-conjugacy class-Griesmer bound-integer linear program-linear code-prescribed automorphism group-projective code-projective set-rational canonical form-two-weightcode