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On the non-existence of a projective (75, 4,12, 5) set in PG(3, 7) |
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| Authors: | Aaron C. S. Chan James A. Davis Jonathan Jedwab |
| Affiliation: | 1. Department of Combinatorics and Optimization, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada 2. Department of Mathematics and Computer Science, University of Richmond, Richmond, VA, 23173, USA 3. Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada |
| Abstract: | 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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