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.
Copyright © 2010, SP Birkhäuser Verlag Basel.
The definitive version is available at: http://link.springer.com/article/10.1007/s00022-010-0041-3
Chan, Aaron C.S., James A. Davis, and Jonathan Jedwab. "On the Non-Existence of a Projective (75, 4, 12, 5) Set in PG(3, 7)." Journal of Geometry 97, no. 1 (April 2010): 29-44. doi:10.1007/s00022-010-0041-3.
Chan, Aaron C.S.; Davis, James A.; and Jedwab, Jonathan, "On the non-existence of a projective (75, 4,12, 5) set in PG(3, 7)" (2010). Department of Math & Statistics Faculty Publications. 152.