1,564 research outputs found
Barwick, W J Brisbane, QX20025
No full textThis record was harvested from a previous catalogue system and will be withdrawn in 2025. Information in this record may be superseded or incomplete. Visit this record in UMA's new catalogue at: https://archives.library.unimelb.edu.au/nodes/view/370533Surname: BARWICK
Given Name(s) or Initials: W J BRISBANE
Military Service Number or Last Known Location: QX20025
Missing, Wounded and Prisoner of War Enquiry Card Index Number: 23583180793
Item: [2016.0049.02860] "Barwick, W J Brisbane, QX20025
A characterisation of tangent subplanes of PG(2, q (3))
No full textIn “Barwick and Jackson (Finite Fields Appl. 18:93–107 2012)”, the authors determine the representation of Order-q-subplanes s and order-q-sublines of PG(2, q³) in the Bruck–Bose representation in PG(6, q). In particular, they showed that an Order-q-subplanes of PG(2, q³) corresponds to a certain ruled surface in PG(6, q). In this article we show that the converse holds, namely that any ruled surface satisfying the required properties corresponds to a tangent Order-q-subplanes of PG(2, q³).S. G. Barwick, Wen-Ai Jackso
An optimal multisecret threshold scheme construction
No full textThe original publication can be found at www.springerlink.comA multisecret threshold scheme is a system which protects a number of secret keys among a group of n participants. There is a secret sK associated with every subset K of k participants such that any t participants in K can reconstruct the secret sK, but a subset of w participants cannot get any information about a secret they are not associated with. This paper gives a construction for the parameters t = 2, k = 3 and for any n and w that is optimal in the sense that participants hold the minimal amount of information.S. G. Barwick and Wen-Ai Jackso
Characterising pointsets in PG(4,q) that correspond to conics
No full textReceived: 23 November 2014 / Revised: 8 April 2015 / Accepted: 1 May 2015 / Published online: 20 May 2015We consider a non-degenerate conic in PG(2,q2), q odd, that is tangent to ℓ∞ and look at its structure in the Bruck–Bose representation in PG(4,q). We determine which combinatorial properties of this set of points in PG(4,q) are needed to reconstruct the conic in PG(2,q2). That is, we define a set C in PG(4,q) with q2 points that satisfies certain combinatorial properties. We then show that if q≥7, we can use C to construct a regular spread S in the hyperplane at infinity of PG(4,q), and that C corresponds to a conic in the Desarguesian plane P(S)≅PG(2,q2) constructed via the Bruck–Bose correspondence.S. G. Barwick, Wen-Ai Jackso
Geometric constructions of optimal linear perfect hash families
No full textA linear (qd,q,t)-perfect hash family of size s in a vector space V of order qd over a field F of order q consists of a sequence 1,…,s of linear functions from V to F with the following property: for all t subsets XV there exists i{1,…,s} such that i is injective when restricted to F. A linear (qd,q,t)-perfect hash family of minimal size d(t−1) is said to be optimal. In this paper we use projective geometry techniques to completely determine the values of q for which optimal linear (q3,q,3)-perfect hash families exist and give constructions in these cases. We also give constructions of optimal linear (q2,q,5)-perfect hash families.S.G. Barwick, and Wen-Ai Jackso
A sequence approach to linear perfect hash families
No full textA linear (q d, q, t)-perfect hash family of size s in a vector space V of order q d over a field F of order q consists of a set S = {φ1, ⋯, φs} of linear functionals from V to F with the following property: for all t subsets X\subseteq V there exists φi ∈ S such that φi is injective when restricted to F. A linear (q d, q, t)-perfect hash family of minimal size d(t - 1) is said to be optimal. In this paper, we extend the theory for linear perfect hash families based on sequences developed by Blackburn and Wild. We develop techniques which we use to construct new optimal linear (q 2, q, 5)-perfect hash families and (q 4, q, 3)-perfect hash families. The sequence approach also explains a relationship between linear (q 3, q, 3)-perfect hash families and linear (q 2, q, 4)-perfect hash families. © 2007 Springer Science+Business Media, LLC.Susan G. Barwick and Wen-Ai Jackso
Sublines and subplanes of PG(2, q(3)) in the Bruck-Bose representation in PG(6, q)
No full textIn this article we look at the Bruck-Bose representation of PG(2,q 3) in PG(6,q). We look at sublines and subplanes of order q in PG(2,q 3) and describe their representation in PG(6,q). We then show how these results can be generalized to the Bruck-Bose representation of PG(2,q n) in PG(2n,q). © 2011 Elsevier Inc. All rights reserved.S.G. Barwick, Wen-Ai Jackso
Optimal linear perfect hash families with small parameters
No full textThe definitive version may be found at www.wiley.comA linear (qd, q, t)-perfect hash family of size s consists of a vector space V of order qd over a field F of order q and a sequence Φ1; . . . ; Φs of linear functions from V to F with the following property: for all t subsets X ⊆ V, there exists i ∈ {1; . . . ; s} such that Φi is injective when restricted to F. A linear (qd, q, t)--perfect hash family of minimal size d(t - 1) is said to be optimal. In this paper, we prove that optimal linear (qd, q, t)-perfect hash families exist only for q = 11 and for all prime powers q > 13 and we give constructions for these values of q.S. G. Barwick, Wen-Ai Jackson and Catherine T. Quin
Size of broadcast in threshold schemes with disenrollment
No full textThreshold schemes are well-studied cryptographic primitives for distributing information among a number of entities in such a way that the information can only be recovered if a threshold of entities co-operate. Establishment of a threshold scheme involves an initialisation overhead. Threshold schemes with disenrollment capability are threshold schemes that enable entities to be removed from the initial threshold scheme at less communication cost than that of establishing a new scheme. We prove a revised version of a conjecture of Blakley, Blakley, Chan and Massey by establishing a bound on the size of the broadcast information necessary in a threshold scheme with disenrollment capability that has minimal entity information storage requirements. We also investigate the characterisation of threshold schemes with disenrollment that meet this bound.S. G. Barwick, W. -A. Jackson, Keith M. Martin, Peter R. Wil
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