Name
Abstract | ||
|---|---|---|
In this paper, we study the weighted (x(q + 1), x; 2, q)-minihypers. These are weighted sets of x(q + 1) points in PG(2, q) intersecting every line in at least x points. We investigate the decomposability of these minihypers, and define a switching construction which associates to an (x(q + 1), x; 2, q)-minihyper, with x 驴 q 2 驴 q, not decomposable in the sum of another minihyper and a line, a (j(q + 1), j; 2, q)-minihyper, where j = q 2 驴 q 驴 x, again not decomposable into the sum of another minihyper and a line. We also characterize particular (x(q + 1), x; 2, q)-minihypers, and give new examples. Additionally, we show that (x(q + 1), x; 2, q)-minihypers can be described as rational sums of lines. In this way, this work continues the research on (x(q + 1), x; 2, q)-minihypers by Hill and Ward (Des Codes Cryptogr 44:169---196, 2007), giving further results on these minihypers. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1007/s10623-009-9314-y | Des. Codes Cryptography |
Keywords | Field | DocType |
Minihypers,Multisets,Griesmer bound | Discrete mathematics,Combinatorics,Mathematics,Griesmer bound | Journal |
Volume | Issue | ISSN |
54 | 2 | 0925-1022 |
Citations | PageRank | References |
2 | 0.44 | 5 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ivan Landjev | 1 | 28 | 5.17 |
| Leo Storme | 2 | 197 | 38.07 |