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A study of (x(q+1),x;2,q)-minihypers

Ivan Landjev and Leo Storme (UGent)
(2010) DESIGNS CODES AND CRYPTOGRAPHY. 54(2). p.135-147
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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 <= q(2) - q, not decomposable in the sum of another minihyper and a line, a (j (q + 1), j; 2, q)-minihyper, where j = q(2) - q-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.
Keywords
Multisets, Minihypers, Griesmer bound, MAXIMAL ARCS, 2, T, PLANE, ORDER

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MLA
Landjev, Ivan, and Leo Storme. “A Study of (x(Q+1),x;2,q)-Minihypers.” DESIGNS CODES AND CRYPTOGRAPHY, vol. 54, no. 2, 2010, pp. 135–47, doi:10.1007/s10623-009-9314-y.
APA
Landjev, I., & Storme, L. (2010). A study of (x(q+1),x;2,q)-minihypers. DESIGNS CODES AND CRYPTOGRAPHY, 54(2), 135–147. https://doi.org/10.1007/s10623-009-9314-y
Chicago author-date
Landjev, Ivan, and Leo Storme. 2010. “A Study of (x(Q+1),x;2,q)-Minihypers.” DESIGNS CODES AND CRYPTOGRAPHY 54 (2): 135–47. https://doi.org/10.1007/s10623-009-9314-y.
Chicago author-date (all authors)
Landjev, Ivan, and Leo Storme. 2010. “A Study of (x(Q+1),x;2,q)-Minihypers.” DESIGNS CODES AND CRYPTOGRAPHY 54 (2): 135–147. doi:10.1007/s10623-009-9314-y.
Vancouver
1.
Landjev I, Storme L. A study of (x(q+1),x;2,q)-minihypers. DESIGNS CODES AND CRYPTOGRAPHY. 2010;54(2):135–47.
IEEE
[1]
I. Landjev and L. Storme, “A study of (x(q+1),x;2,q)-minihypers,” DESIGNS CODES AND CRYPTOGRAPHY, vol. 54, no. 2, pp. 135–147, 2010.
@article{978923,
  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 <= q(2) - q, not decomposable in the sum of another minihyper and a line, a (j (q + 1), j; 2, q)-minihyper, where j = q(2) - q-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.}},
  author       = {{Landjev, Ivan and Storme, Leo}},
  issn         = {{0925-1022}},
  journal      = {{DESIGNS CODES AND CRYPTOGRAPHY}},
  keywords     = {{Multisets,Minihypers,Griesmer bound,MAXIMAL ARCS,2,T,PLANE,ORDER}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{135--147}},
  title        = {{A study of (x(q+1),x;2,q)-minihypers}},
  url          = {{http://doi.org/10.1007/s10623-009-9314-y}},
  volume       = {{54}},
  year         = {{2010}},
}

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