Physical Sciences and Mathematics Commons^™

On Circulant Weighing Matrices, K. T . Arasu, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

Algebraic techniques are employed to obtain necessary conditions for the existence of certain circulant weighing matrices. As an application we rule out the existence of many circulant weighing matrices. We study orders n = s2 + s + 1, for 10 less than or equal to s less than or equal to 25. These orders correspond to the number of points in a projective plane of order s.

Group Divisible Designs, Gbrsds And Generalized Weighing Matrices, D. G. Sarvate, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

We give new constructions for regular group divisible designs, pairwise balanced designs, generalized Bhaskar Rao supplementary difference sets and generalized weighing matrices. In particular if p is a prime power and q divides p – 1 we show the following exist:

(i) GDD(2(p2 +p+ 1), 2(p2 +p+ 1), rp2, 2p2, λ1 = p2λ, λ2 = (p2 —p)r, m = p2 + p+ 1, n = 2), r = 1,2;

(ii) GDD(q(p+ 1), q(p+ 1), p(q – 1), p(q –1), λ1 = (q – 1)(q – 2), λ2 = (p– 1)(q – 1)2/q, m = q, n = p+1);

(iii) PBD(21, …

Bayesian Hierarchical Analysis Of Minefield Data, Noel A. Cressie, Andrew B. Lawson

Faculty of Informatics - Papers (Archive)

Based on remote sensing of a potential minefield, point locations are identified, some of which may not be mines. The mines and mine-like objects are to be distinguished based on their point patterns, although it must be emphasized that all we see is the superposition of their locations. In this paper, we construct a hierarchical spatial point-process model that accounts for the different patterns of mines and mine-like objects and uses posterior analysis to distinguish between them. Our Bayesian approach is applied to COBRA image data obtained from the NSWC Coastal Systems Station, Dahlgren Division, Panama City, Florida. 2003 Copyright …

Letter To The Editor, Noel A. Cressie

Faculty of Informatics - Papers (Archive)

No abstract provided.

On The (10,5,$\Lambda$)-Family Of Bhaskar Rao Designs, Ghulam R. Chaundhry, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

We prove a theorem for BRD(10,5,λ)s and give thirteen (13) inequivalent BRD(10,5,4)s 

An Experimental Search And New Combinatorial Designs Via A Generalisation Of Cyclotomy, Marc Gysin, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

Cyclotomy can be used to construct a variety of combinatorial designs, for example, supplementary difference sets, weighing matrices and T -matrices. These designs may be obtained by using linear combinations of the incidence matrices of the cyclotomic cosets. However, cyclotomy only works in the prime and prime power cases. We present a generalisation of cyclotomy and introduce generalised cosets. Combinatorial designs can now be obtained by a search through all linear combinations of the incidence matrices of the generalised cosets. We believe that this search method is new. The generalisation works for all cases and is not restricted to prime …

Some Necessary And Sufficient Conditions For Two Variable Orthogonal Designs In Order 44, Christos Koukouvinos, M. Mitrouli, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

We give a new algorithm which allows us to construct new sets of sequences with entries from the commuting variables 0, ±a, ±b, ±c, ±d with zero autocorrelation function. We show that for twelve cases if the designs exist they cannot be constracted using four circulant matrices in the Goethals-Seidel array. Further we show that the necessary conditions for the existence of an OD(44;s₁,s₂) are sufficient except possibly for the following 7 cases. (7,32) (8,31) (9,30) (9,33) (11,30) (13,29) (15,26) which could not be found because of the large size of the search space for a …

Bose's Method Of Differences Applied To Construct Bhaskar Rao Designs, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

In this paper we show that BIBD(v,b,r,k,λ) where v = pq or pq + 1, when written in the notation of Bose's method of differences may often be used to find generalized Bhaskar Rao designs GBRD(p,b',r',k,λ;G) where G is a group of order q and vice versa. This gives many new GBRDs including a GBRD(9,5,5;Z₅) and a GBRD(13,7,7;Z₇).

Infinite Families Of Generalized Bhaskar Rao Designs, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

We show that GBRD(p,¹/₂(p-1), ¹/₈(p-1)(p-3);EA(¹/₂p-1)) exist for all prime powers p ≡ 3 (mod 4). We also show that GBRD(p,¹/₂(p - 1), ¹/₄(p - 1)(p - 3); EA(¹/₂(p - 1)) exist for all prime powers p ≡ 1 (mod 4).

This allows us to give a new proof that a BIBD(f(ef + 1),(ef + 1)(ef² + f -1),ef + f -1,f,f - 1) exists whenever p = ef + 1 is a prime power. This gives many …

Group Divisible Designs, Gbrdsds And Generalized Weighing Matrices, Dinesh G. Sarvate, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

We give new constructions for regular group divisible designs, pairwise balanced designs, generalized Bhaskar Rao supplementary difference sets and generalized weighing matrices. In particular if p is a prime power and q divides p - 1 we show the following exist;

(i) GDD (2(p²+p+1), 2(p²+p+1), rp²,2p², λ1 = p²λ, λ2 = (p²-p)r, m=p²+p+1,n=2), r_+1,2;

(ii) GDD(q(p+1), q(p+1), p(q-1), p(q-1),λ1=(q-1)(q-2), λ₂=(p-1)(q-1)²/q,m=q,n=p+1);

(iii) PBD(21,10;K),K={3,6,7} and PDB(78,38;K), K={6,9,45};

(iv) GW(vk,k²;EA(k)) whenever a (v,k,λ)-difference set exists and k is a prime power;

(v) PBIBD(vk …

Numerical Algorithms For The Computation Of The Smith Normal Form Of Integral Matrices,, C. Koukouvinos, M. Mitrouli, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

Numerical algorithms for the computation of the Smith normal form of integral matrices are described. More specifically, the compound matrix method, methods based on elementary row or column operations and methods using modular or p-adic arithmetic are presented. A variety of examples and numerical results are given illustrating the execution of the algorithms.

Posets And Differential Graded Algebras, Jacqueline Ramagge, Wayne W. Wheeler

Faculty of Informatics - Papers (Archive)

If P is a partially ordered set and R is a commutative ring, then a certain differential graded /f-algebra A,(P) is defined from the order relation on P. The algebra A.(Vi) corresponding to the empty poset is always contained in A.(P) so that A,(P) can be regarded as an /4.(0)-algebra. The main result of this paper shows that if R is an integral domain and P and P' are finite posets such that A.(P) = A.(P') as differential graded /4,(0)-algebras, then P and P' are isomorphic. 1991 Mathematics subject classification (Amer. Math. Soc): primary 06A06.

A Haagerup Inequality For A1 X A1 And A2 Buildings, Jacqueline Ramagge, Guyan Robertson, Tim Steger

Faculty of Informatics - Papers (Archive)

Haagerup's inequality for convolvers on free groups may be interpreted as a result on A₁ buildings, i.e. trees. Here are proved analogous inequalities for discrete groups acting freely on the vertices of A₁ x A₁ and A₂ buildings. The results apply in particular to groups of typerotating automorphisms acting simply transitively on the vertices of such buildings. These results provide the first examples of higher rank groups with property (RD).

Image Compression Based On Genealogical Relation Of The Tsvq Indices, Jamshid Shanbehzadeh, Philip Ogunbona, Abdoihosein Sarafzadeh

Faculty of Informatics - Papers (Archive)

The indices obtained by tree-structured vector quantisation (TSVQ) have an interesting property that enables them to give information about the correlation between two image blocks. Iftwo image blocks are highly correlated, they may have an identical index, or the same ancestors. The existence of high inter-block correlation in natural images results in having neighboring blocks with the same genealogy. This characteristic can be used to compress the indices. This paper introduces a novel method to exploit the genealogical relation between the image block indices obtained from a TSVQ. The performance of this scheme in terms of PSNR versus average rate …

Covert Distributed Computing Using Java Through Web Spoofing, J. Horton, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

We use the Web Spoofing attack reported by Cohen and also the Secure Internet Programming Group at Princeton University to give a new method of achieving covert distributed computing with Java. We show how Java applets that perform a distributed computation can be inserted into vulnerable Web pages. This has the added feature that users can rejoin a computation at some later date through bookmarks made while the pages previously viewed were spoofed. Few signs of anything unusual can be observed. Users need not knowingly revisit a particular Web page to be victims. We also propose a simple countermeasure against …

Bose's Method Of Differences Applied To Construct Bhaskar Rao Designs, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

In this paper we show that BIBD(v, b, r, k, λ), where v = pq or pq + 1, when written in the notation of Bose's method of differences may often be used to find generalized Bhaskar Rao designs GBRD(p, b', r', k, λ; G) where G is a group of order q and vice versa. This gives many new GBRDs including a GBRD(9, 5, 5; Z5) and a GBRD(13, 7, 7; Z7).

Equitable Key Escrow With Limited Time Span (Or, How To Enforce Time Expiration Cryptographically), M. Burmester, Y. Desmedt, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

With equitable key escrow the control of society over the individual and the control of the individual over society are shared fairly. In particular, the control is limited to specified time periods. We consider two applications: time controlled key escrow and time controlled auctions with closed bids. In the first the individual cannot be targeted outside the period authorized by the court. In the second the individual cannot withhold his closed bid beyond the bidding period. We propose two protocols, one for each application. We do not require the use of temper-proof devices.

The Translation Planes Of Order 49 And Their Automorphism Groups, C. Charnes, U. Dempwolff

Faculty of Informatics - Papers (Archive)

Using isomorphism invariants, we enumerate the translation planes of order 49 and determine their automorphism groups.

On The (10, 5, Λ)-Family Of Bhaskar Rao Designs, G. Chaudhry, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

We prove a theorem for BRD(10,5,Lambda)s and give thirteen (13) inequivalent BRD(10,5,4)s.

Perfect Secret Sharing Schemes From Room Squares, G. R. Chaudhry, H Ghodosi, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

Secret sharing schemes are one of the most important primitives in distributed systems. In perfect secret sharing schemes, collaboration between unauthorised participants cannot reduce their uncertainty about the secret. This paper presents a perfect secret sharing scheme arising from critical sets of Room squares.

On New Families Of Supplementary Difference Sets Over Rings With Short Orbits, M. Gysin, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

We discuss difference sets (DS) and supplementary difference sets (SDS) over rings. We survey some constructions of SDS over Galois rings where there are no short orbits. ,From there we move to constructions which involve short orbits. These give rise to new infinite families of SDS over GF(p) x GF(q), p, q both prime powers. Many of these families have λ = 1. We also show some new balanced incomplete block designs and pairwise balanced designs arising from the constructions given here.

Necessary And Sufficient Conditions For Some Two Variable Orthogonal Designs In Order 44, C. Koukouvinos, M. Mitrouli, Jennifer Seberry

Faculty of Informatics - Papers (Archive)

We give a new algorithm which allows us to construct new sets of sequences with entries from the commuting variables 0, ± a, ± b, ± c, ± d with zero autocorrelation function. We show that for twelve cases if the designs exist they cannot be constracted using four circulant matrices in the Goethals-Seidel array. Further we show that the necessary conditions for the existence of an OD(44; s1, s2) are sufficient except possibly for the following 7 cases: (7, 32) (8, 31), (9, 30) (9, 33) (11,30) (13, 29) (15, 26) which could not be found because of the …