The minimum volume of subspace trades Full article
| Journal |
Discrete Mathematics
ISSN: 0012-365X , E-ISSN: 1872-681X |
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| Output data | Year: 2017, Volume: 340, Number: 12, Pages: 2723-2731 Pages count : 9 DOI: 10.1016/j.disc.2017.08.012 | ||
| Tags | Bitrades, Trades, Subspace designs | ||
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Abstract:
A subspace bitrade of type Tq(t,k,v) is a pair (T0,T1) of two disjoint nonempty collections of k-dimensional subspaces of a v-dimensional space V over the finite field of order q such that every t-dimensional subspace of V is covered by the same number of subspaces from T0 and T1. In a previous paper, the minimum cardinality of a subspace Tq(t,t+1,v) bitrade was established. We generalize that result by showing that for admissible v, t, and k, the minimum cardinality of a subspace Tq(t,k,v) bitrade does not depend on k. An example of a minimum bitrade is represented using generator matrices in the reduced echelon form. For t=1, the uniqueness of a minimum bitrade is proved.
Cite:
Krotov D.S.
The minimum volume of subspace trades
Discrete Mathematics. 2017. V.340. N12. P.2723-2731. DOI: 10.1016/j.disc.2017.08.012 WOS Scopus РИНЦ OpenAlex
The minimum volume of subspace trades
Discrete Mathematics. 2017. V.340. N12. P.2723-2731. DOI: 10.1016/j.disc.2017.08.012 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jun 28, 2016 |
| Accepted: | Aug 8, 2017 |
| Published online: | Sep 5, 2017 |
Identifiers:
| Web of science: | WOS:000412621100001 |
| Scopus: | 2-s2.0-85028750380 |
| Elibrary: | 31064594 |
| OpenAlex: | W2270759269 |