@article { ,
title = {The lines of PG(4, 2) are the points on a quintic in PG(9,2)},
abstract = {Let V denote a 5-dimensional vector space over a field, and let (bij) denote the 10 independent components of a bivectorb?\Λ2Vrelative to a choice of product basis \{ei\Λej: 1 \≤i\<j\≤ 5\} for\Λ2V. It is well known thatb(\≠ 0) is decomposable (pure, simple) if and only if its componentsbijsatisfy a set of five quadratic conditions resulting from the Grassmann relations. In the case= GF(2) it is shown that these five quadratic conditions are equivalent to a single quintic condition. In projective language the 155 lines of PG(4, 2) are therefore seen to be (in 1-1 correspondence with) the 155 points on a certain quintic lying in PG(9, 2).},
doi = {10.1016/0097-3165(94)90102-3},
issn = {0097-3165},
issue = {1},
journal = {Journal of Combinatorial Theory, Series A},
note = {Batch 005. Output ID 37176. Interdisciplinary research is No, but Unit of Assessment has been selected. One of these needs to change. (16.12.11)},
pages = {226-231},
publicationstatus = {Published},
publisher = {Elsevier},
url = {https://hull-repository.worktribe.com/output/405480},
volume = {68},
keyword = {Theoretical Computer Science, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics},
year = {1994},
author = {Shaw, Ron and Gordon, Neil A}
}