Last modified: October 13, 2014
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Here is a list of publications, including a few that are not refereed,
dated October 2014: Bill's publications.
Let's begin with the most recent:
Submitted for publication:
- ``Linking systems in nonelementary abelian groups''
(with Jim Davis and John Polhill).
J. Combin. Theory Ser. A
123, no. 1 (2014), pp. 92-103.
- ``Uniformity in association schemes and coherent configurations: cometric Q-antipodal schemes and linked systems'' (with Edwin van Dam and Mikhail Muzychuk).
Combinatorial Theory, Series A 120, Issue 7, September 2013,
- ``Enhanced Flexibility for Homomorphic Encryption Schemes via CRT
'' (with Yin Hu and Berk Sunar). Industrial Track of ACNS '12, 10th
International Conference on Applied Cryptography and Network Security ,
June 26-29, 2012, Singapore.
- ``Characterizing completely regular codes from an
algebraic viewpoint'' (with Jack Koolen and Woosun Lee),
and Graphs Contemporary
Mathematics (Vol. 531) Richard A. Brualdi, Samad Hedayat,
Hadi Kharaghani, Gholamreza B. Khosrovshahi, and Shahriar Shahriari, editors.
Published by the American Mathematical Society, 2010.
- ``On the equivalence between real mutually unbiased bases
and a certain class of association schemes'' (with Nick LeCompte and Will Owens).
European Journal of Combinatorics 31, no. 6 (2010), pp. 1499-1512.
- ``Resilient functions: Just how resilient are the they?'' (with Berk Sunar), in:
Error-Correcting Codes, Finite Geometries and Cryptography Contemporary Mathematics, Vol. 523 Aiden A. Bruen, and David L. Wehlau, editors. Published by the American Mathematical Society, 2010.
- ``Commutative association schemes'' (with Hajime Tanaka).
European Journal of Combinatorics 30, no. 6 (2009), pp. 1497-1525.
- ``There are finitely many Q-polynomial association
schemes with given first multiplicity at least three.''
(with Jason Williford).
European Journal of Combinatorics 30, no. 3 (2009), pp. 698-704.
- ``Representations of directed strongly regular graphs.''
(with C. D. Godsil and Sylvia
Hobart.) European Journal of Combinatorics 28 no. 7 (2007), 1980--1993.
(Proceedings of "Geometric and Algebraic Combinatorics 3".)
- ``Imprimitive cometric association schemes:
constructions and analysis.''
(with Mikhail Muzychuk and
Journal of Algebraic Combinatorics 25 no. 4 (2007), 399--415.
- ``A provably secure true random number generator with
built-in tolerance to active attacks.''
(with B. Sunar and
IEEE Transactions on Computers 56 no. 1 (2007), 109--119.
- ``A dual Plotkin bound for (T,M,S)-nets''
(with Terry Visentin) IEEE Trans. Inform. Theory, 53, no. 1 (2007), 411-415..
- ``(t,m,s)-Nets'' in: CRC Handbook
of Combinatorial Designs, 2nd ed. (C. Colbourn and J. Dinitz, eds.), CRC
Press, Boca Raton, FL, 2006.
- PDF file (142K)
- MinT a database of the latest
information about constructions and bounds for (t,m,s)-nets,
maintained at the University of Salzburg by Rudi Schurer and Wolfgang Schmid.
- ``Some new constructions of imprimitive cometric association
(with Mikhail Muzychuk and
Proceedings, "Algebraic Combinatorics",
an international conference in honour of Eiichi Bannai's 60th birthday,
June 26-30, 2006, Sendai International Center, Sendai, Japan (not refereed).
- ``Linear programming bounds for $(T,M,S)$-nets''
(extended abstract), Proceedings of the Seventh Asian Symposium on Computer
Mathematics, Seoul, Republic of Korea, December 2005.
- ``A new notion of transitivity for groups and
sets of permutations.''
B. E. Sagan) Journal of the London Mathematical Society, 73
(2006), 1-13 .
- ``Completely regular codes: a viewpoint
and some problems.'' pages 43--56 in: Proceedings
of 2004 Com2MaC Workshop on Distance-Regular Graphs and Finite Geometry,
July 24 - 26, 2004, Pusan, Korea (invited, not refereed).
- ``A physics-free introduction to quantum
error-correcting codes.'' Utilitas Mathematica, 65
- ``Width and dual width of subsets in
polynomial association schemes.'' (with A. E. Brouwer, C. D. Godsil
and J. Koolen) Journal of Combinatorial Theory, Series A 102
- ``Symmetric designs, sets with two intersection
numbers, and Krein parameters of incidence graphs''
Journal of Combin. Math. and Combin. Computing 38 (2001),
- ``Design systems: combinatorial characterizations of
Delsarte T-designs via partially ordered sets.'' pp. 223-239,
in: Codes and Association Schemes DIMACS Series in Discrete
Mathematics and Theoretical Computer Science, vol. 56, (A. Barg
and S. Litsyn, eds.) American Mathematical Society, 2001.
- ``Minimum distance bounds for
Designs, Codes, and Crypt. 21, Issue 1/3 (2000), 181-187.
(Proceedings of the conference ``GEOMETRIC AND ALGEBRAIC
COMBINATORICS'' in honour of the 80th birthday of J.J. Seidel,
August 15-20, 1999.)
- ``Linear programming bounds for ordered orthogonal
arrays and (T,M,S)-nets.'' pp. 368--376, in:
Monte Carlo and Quasi-Monte Carlo Methods 1998: Proceedings of a
Conference held at the Claremont Graduate University,
Claremont, California, USA, June 22-26, 1998. H. Niederreiter and
J. Spanier, eds.
- ``Association schemes for ordered orthogonal
arrays and (T,M,S)-nets.'' (with
Canad. J. Math. 51, no. 2
- ``A generalized Rao bound for ordered orthogonal
arrays and (t,m,s)-nets.'' (with
Canadian Math. Bulletin 42, no. 3
- ``Designs in product association schemes,''
Designs, Codes, and Crypt. 16, no. 3 (1999), 271-289.
- ``Completely regular designs,''
J. Combin. Designs
6, no. 4 (1998), 261-273.
- ``Mixed block designs,''
J. Combin. Designs
6, no. 2 (1998), 151-163.
- ``The stipulation polynomial of a uniquely list-colorable graph,''
Australasian J. Combin. 11 (1995), 105-115.
- ``Anticodes for the Grassman [sic] and bilinear forms graphs,''
(with X.J. Zhu)
Designs, Codes, and Crypt. 6, no. 1 (1995), 73-79.
- ``Quotients of association schemes,'' (with
J. Combin. Th., Ser. A
69, no. 2 (1995), 185-199.
- ``Completely regular designs of strength one,'' J. Alg. Combin.
3 (1994), 177-185.
Some projects in progress:
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