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On small blocking sets and their linearity

Peter Sziklai
2008 Journal of combinatorial theory. Series A  
We prove that a small minimal blocking set of PG(2, q) is "very close" to be a linear blocking set over some subfield GF(p e ) < GF(q).  ...  This implies that (i) a similar result holds in PG(n, q) for small minimal blocking sets with respect to k-dimensional subspaces (0 k n) and (ii) most of the intervals in the interval-theorems of Szőnyi  ...  In Section 3 the known bounds and structure results on small blocking sets are enlisted.  ... 
doi:10.1016/j.jcta.2008.01.006 fatcat:whgd74xfwndx3kvqx3lwf7ieg4

On the stability of small blocking sets

Tamás Szőnyi, Zsuzsa Weiner
2013 Journal of Algebraic Combinatorics  
A stability theorem says that a nearly extremal object can be obtained from an extremal one by "small changes". In this paper, we study the relation of sets having few 0-secants and blocking sets.  ...  A blocking set is minimal, when no proper subset of it is a blocking set.  ...  Many of them concentrate on small blocking sets of PG (2, q) , these are blocking sets whose cardinality is less than 3 2 (q + 1).  ... 
doi:10.1007/s10801-013-0487-0 fatcat:q5ldvbcixvfntj3zpkoewhaf5m

On Small Sets of Distribution Functions of Ratio Block Sequences

David Krčmarský, Ladislav Mišík, Zuzana Václavíková
2016 Uniform Distribution Theory  
One of the most interesting is that using the set of all distribution functions of the corresponding ratio block sequence introduced in [Strauch, O.—Tóth, J.T.: Publ. Math.  ...  In the present paper we give some sufficient conditions under which this set is small in a metric sense. As a corollary we obtain a new characterization of the case of asymptotic distribution.  ...  One of the most challenging open problem of theory of sets of distribution functions of ratio block sequences is that of characterization of all possible sets G(X n ), see [SN] .  ... 
doi:10.1515/udt-2016-0009 fatcat:fjlw76okqbcvthdkjt7rzf4tiy

Characterization results on small blocking sets of the polar spaces Q +(2n + 1, 2) and Q +(2n + 1, 3)

J. De Beule, K. Metsch, L. Storme
2007 Designs, Codes and Cryptography  
In [8] , De Beule and Storme characterized the smallest blocking sets of the hyperbolic quadrics Q + (2n + 1, 3), n ≥ 4; they proved that these blocking sets are truncated cones over the unique ovoid of  ...  This means that the two smallest minimal blocking sets of Q + (2n + 1, 2), n ≥ 3, are classified.  ...  The lines on S meeting B form a minimal blocking set in the quotient geometry on S (Corollary 2.2). This blocking set is not an ovoid, since the lines SR 1 and SR 2 are perpendicular.  ... 
doi:10.1007/s10623-007-9087-0 fatcat:xpevzo3okngzhnc3f7cbhmopbe

Manufacturing optimization using Tsukamoto fuzzy inference system method: A case study in block paving and solid concrete block industry

M Sayuti, Juliananda, Diana Khairani Sofyan, P. Puspitasari, A.H. Suryanto, T. Lenggo Ginta, I. Srikun, A. Ayu Permanasari, M. Niaz Akhtar, M. Sharifi Jebeli, Y. Rohmat Aji Pradana, D. Zakariya Lubis (+2 others)
2018 MATEC Web of Conferences  
While the number of block paving produced by the company on the period of  ...  From the calculations, the number of solid concrete block produced by the company on the period of October 2016, December 2016 and February 2017 was not optimal.  ...  Kawan Setia is one of the manufacturing companies engaged in the manufacture of solid concrete block and block paving.  ... 
doi:10.1051/matecconf/201820402002 fatcat:gkcpbrdbibeoxcyiuroo4xkuaa

Small-LRU: A Hardware Efficient Hybrid Replacement Policy

Purnendu Das, Bishwa Ranjan
2020 International Journal of Advanced Computer Science and Applications  
Modern LLCs are divided into multiple banks where each bank is a set-associative cache.  ...  The replacement policy implemented on such highly associative banks consume significant hardware (storage and area) overhead.  ...  To insert a newly incoming block in the set, one of the existing block need to be evicted first known as the victim block.  ... 
doi:10.14569/ijacsa.2020.0110981 fatcat:dyrh76k575dtbbwzo6xinuz4ia

A small minimal blocking set in PG(n, p t ), spanning a (t − 1)-space, is linear

Peter Sziklai, Geertrui Van de Voorde
2012 Designs, Codes and Cryptography  
In this paper, we show that a small minimal blocking set with exponent e in PG(n, p t ), p prime, spanning a (t/e − 1)-dimensional space, is an F p e -linear set, provided that p > 5(t/e) − 11.  ...  As a corollary, we get that all small minimal blocking sets in PG(n, p t ), p prime, p > 5t − 11, spanning a (t − 1)-dimensional space, are F p -linear, hence confirming the linearity conjecture for blocking  ...  A blocking set B is called small if |B| < 3(q + 1)/2 and minimal if no proper subset of B is a blocking set.  ... 
doi:10.1007/s10623-012-9751-x fatcat:62xiejltr5a5fnmaapuryllpru

On the linearity of higher-dimensional blocking sets [article]

Geertrui Van de Voorde
2012 arXiv   pre-print
A small minimal k-blocking set B in PG(n, q), q = pt, p prime, is a set of less than 3(qk + 1)/2 points in PG(n, q), such that every (n - k)-dimensional space contains at least one point of B and such  ...  Furthermore, we show that the linearity of small minimal blocking sets in PG(2, q) implies the linearity of small minimal k-blocking sets in PG(n, pt), with exponent e, with pe \geq t/e + 11.  ...  Previous results In this section, we list a few results on the linearity of small minimal k-blocking sets and on the size of small k-blocking sets that will be used throughout this paper.  ... 
arXiv:1201.3300v1 fatcat:asrb2yuto5finiapgccwhtq6f4

Constructing minimal blocking sets using field reduction [article]

Geertrui Van de Voorde
2015 arXiv   pre-print
of the blocking cone over a planar blocking set, we obtain larger blocking sets than the ones obtained from planar blocking sets in pol.  ...  We show that if a small minimal blocking set is constructed from the MPS-construction, it is of Rédei-type whereas a small minimal blocking set arises from our cone construction if and only if it is linear  ...  This also provides us with a different view on the linearity conjecture for small minimal blocking sets.  ... 
arXiv:1512.04822v1 fatcat:xqdxixcdebgj3nocrgr2n3gyou

Small point sets of PG(n, p 3h ) intersecting each line in 1 mod p h points

Nóra V. Harrach, Klaus Metsch, Tamás Szőnyi, Zsuzsa Weiner
2010 Journal of Geometry  
sets with respect to lines) are linear blocking sets.  ...  The main result of this paper is that point sets of PG(n, q), q = p 3h , p ≥ 7 prime, of size less than 3(q n−1 + 1)/2 intersecting each line in 1 modulo 3 √ q points (these are always small minimal blocking  ...  Small minimal blocking sets There has been a lot of attention paid on small minimal (planar) blocking sets. Bruen showed that a non-trivial blocking set has size at least q + √ q + 1.  ... 
doi:10.1007/s00022-010-0051-1 fatcat:pylpwnuivngund5m4lerld3jru

Constructing Minimal Blocking Sets Using Field Reduction

Geertrui Van de Voorde
2015 Journal of combinatorial designs (Print)  
of the blocking cone over a planar blocking set, we obtain larger blocking sets than the ones obtained from planar blocking sets in [15] .  ...  We show that if a small minimal blocking set is constructed from the MPSconstruction, it is of Rédei-type whereas a small minimal blocking set arises from our cone construction if and only if it is linear  ...  This also provides us with a different view on the linearity conjecture for small minimal blocking sets.  ... 
doi:10.1002/jcd.21432 fatcat:yxolr5pllzdvvm5a45vt2q7ble

Page 920 of Automation and Remote Control Vol. 37, Issue 6 [page]

1976 Automation and Remote Control  
This distance depends, first, on how the subset of vertices of the initial graph (block) correspond to the vertices of the small graph, and, second, what kind of structure the small graph possesses, To  ...  Muchnik UDC 519.283 Approximation of a graph by one with a small number of vertices, posed in [4], is considered.  ... 

Page 954 of Journal of Cognitive Neuroscience Vol. 12, Issue 6 [page]

2000 Journal of Cognitive Neuroscience  
set of large blocks in the subsequent set of test trials was subtracted from the response to the block that would be matched to the set of small blocks.  ...  As expected, in the initial baseline trials, the difference calculated between estimates of the probe blocks based on whether they were to be matched to the set of large or small key blocks was not significant  ... 

Page 610 of IEEE Transactions on Computers Vol. 52, Issue 5 [page]

2003 IEEE Transactions on Computers  
When particular small block is accessed by the CPU, th corresponding hit bit is set to one. Thus, the hit bit: the small block identifies it as a referenced block 2.  ...  The data in the small block are sent to the CPU and the hit bit is set to mark it as referenced.  ... 

Page 159 of American Society of Civil Engineers. Collected Journals Vol. 3, Issue AE4 [page]

1997 American Society of Civil Engineers. Collected Journals  
15 Epoxy” (one week set), no toe nails 15 Epoxy* (one week set), toe-nailed when epoxy was wet 16 Toe nail + epoxy on small wood blocks’ (one week set) Toe nail + epoxy on small wood blocks (24—48 hr.  ...  set) Toe nail + epoxy on large wood blocks* (one week set) Acrylic adhesive” (one week set), toe-nailed when adhesive was wet Acrylic adhesive” (one week set), wood first soaked 24 h, toe-nailed when  ... 
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