On the gaps of the spectrum of volumes of trades Full article
| Journal |
Journal of Combinatorial Designs
ISSN: 1063-8539 |
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| Output data | Year: 2018, Volume: 26, Number: 3, Pages: 119-126 Pages count : 8 DOI: 10.1002/jcd.21592 | ||
| Tags | minimum volume, Reed–Muller code, t-design, trade | ||
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Abstract:
A pair {T0,T1} of disjoint collections of k-subsets (blocks) of a set V of cardinality v is called a t-(v,k) trade or simply a t-trade if every t-subset of V is included in the same number of blocks of T0 and T1. The cardinality of T0 is called the volume of the trade. Using the weight distribution of the Reed--Muller code, we prove the conjecture that for every i from 2 to t, there are no t-trades of volume greater than 2^{t+1}-2^i and less than 2^{t+1}-2^{i-1} and derive restrictions on the t-trade volumes that are less than 2^{t+1}+2^{t-1}.
Cite:
Krotov D.S.
On the gaps of the spectrum of volumes of trades
Journal of Combinatorial Designs. 2018. V.26. N3. P.119-126. DOI: 10.1002/jcd.21592 WOS Scopus РИНЦ OpenAlex
On the gaps of the spectrum of volumes of trades
Journal of Combinatorial Designs. 2018. V.26. N3. P.119-126. DOI: 10.1002/jcd.21592 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Dec 19, 2016 |
| Accepted: | Oct 14, 2017 |
| Published online: | Nov 1, 2017 |
Identifiers:
| Web of science: | WOS:000419829900002 |
| Scopus: | 2-s2.0-85032834218 |
| Elibrary: | 35476393 |
| OpenAlex: | W3101061236 |