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.

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Post-print Article

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Copyright © 2010, SP Birkhäuser Verlag Basel.

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DOI: 10.1007/s00022-010-0041-3

Full Citation:

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.