On the non-existence of a projective (75, 4,12, 5) set in PG(3, 7)
2
Department of Mathematics and Computer Science, University of Richmond, Richmond, USA
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Publication type: Journal Article
Publication date: 2010-04-01
scimago Q4
wos Q3
SJR: 0.224
CiteScore: 1.0
Impact factor: 0.5
ISSN: 00472468, 14208997
Geometry and Topology
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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Chan A. C. S., Davis J. A., Jedwab J. On the non-existence of a projective (75, 4,12, 5) set in PG(3, 7) // Journal of Geometry. 2010. Vol. 97. No. 1-2. pp. 29-44.
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Chan A. C. S., Davis J. A., Jedwab J. On the non-existence of a projective (75, 4,12, 5) set in PG(3, 7) // Journal of Geometry. 2010. Vol. 97. No. 1-2. pp. 29-44.
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TY - JOUR
DO - 10.1007/s00022-010-0041-3
UR - https://doi.org/10.1007/s00022-010-0041-3
TI - On the non-existence of a projective (75, 4,12, 5) set in PG(3, 7)
T2 - Journal of Geometry
AU - Chan, Aaron C S
AU - Davis, James A.
AU - Jedwab, Jonathan
PY - 2010
DA - 2010/04/01
PB - Springer Nature
SP - 29-44
IS - 1-2
VL - 97
SN - 0047-2468
SN - 1420-8997
ER -
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@article{2010_Chan,
author = {Aaron C S Chan and James A. Davis and Jonathan Jedwab},
title = {On the non-existence of a projective (75, 4,12, 5) set in PG(3, 7)},
journal = {Journal of Geometry},
year = {2010},
volume = {97},
publisher = {Springer Nature},
month = {apr},
url = {https://doi.org/10.1007/s00022-010-0041-3},
number = {1-2},
pages = {29--44},
doi = {10.1007/s00022-010-0041-3}
}
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MLA
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Chan, Aaron C. S., et al. “On the non-existence of a projective (75, 4,12, 5) set in PG(3, 7).” Journal of Geometry, vol. 97, no. 1-2, Apr. 2010, pp. 29-44. https://doi.org/10.1007/s00022-010-0041-3.