Publications

Last modified: October 17, 2017

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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:

not listed

Under Revision:

"On the connectivity of graphs in association schemes" (with Brian Kodalen)
- arXiv:1702.03801

To appear:

Published:

(Not refereed) "On an early paper of Maryam Mirzakhani" Bull. Inst. Combin. Appl. 81 (2017), 42--51.
- arXiv:1709.07540
"Some nonexistence results for strong external difference families using character theory" (with Doug Stinson) Bull. Inst. Combin. Appl. 80 (2017), 79--92.
- arXiv:1610.06432
"Arithmetic using word-wise homomorphic encryption" (with Gizem Cetin, Yarkin Doroz and Berk Sunar) Presented at Arctic Crypt 2016, Longyearbyen, Svalbard, Norway, July 2016.
- Cryptology ePrint Archive: Report 2015/1195
- ``Arithmetic completely regular codes'' (with Jack Koolen, Woosun Lee, and Hajime Tanaka), Discrete Mathematics and Theoretical Computer Science 17 no. 3 (2016), 59--76.
  - Published version
  - arXiv:0911.1826
  - PDF file (425K)
- ``Bounded, yet sufficient? How to determine whether limited side channel information enables key recovery'' (with T.~Eisenbarth and X.~Ye), (preprint) in: Smart Card Research and Advanced Applications Volume 8968 of the series Lecture Notes in Computer Science pp 215-232
- ``On the ideal of the shortest vectors in the Leech lattice and other lattices'' (with Corre Love Steele), arXiv:1310.6626. Journal of Algebraic Combinatorics 41 no. 3 (2015), 707--726.
  - (Revised, July 21, 2014) PDF file (336K)
- ``Linking systems in nonelementary abelian groups'' (with Jim Davis and John Polhill). J. Combin. Theory Ser. A 123, no. 1 (2014), pp. 92-103.
  - PDF file (370K)
- ``Uniformity in association schemes and coherent configurations: cometric Q-antipodal schemes and linked systems'' (with Edwin van Dam and Mikhail Muzychuk). Journal of Combinatorial Theory, Series A 120, Issue 7, September 2013, Pages 1401--1439
  - PDF file (359K) (Draft dated Jan. 27, 2010), arXiv:1001.4928
- ``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.
  - PDF file
- ``Characterizing completely regular codes from an algebraic viewpoint'' (with Jack Koolen and Woosun Lee), arXiv:0911.1828 in: Combinatorics 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.
  - PDF file (287K)
- ``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.
  DOI link: http://dx.doi.org/10.1016/j.ejc.2009.11.014
  - PDF file (206K)
  - Journal preprint access (with subscription)
- ``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.
  - PDF file (503K) (Submitted: November 2, 2009; Revised: Dec. 29, 2009).
- ``Commutative association schemes'' (with Hajime Tanaka). European Journal of Combinatorics 30, no. 6 (2009), pp. 1497-1525.
  DOI link: http://dx.doi.org/10.1016/j.ejc.2008.11.001
  - PDF file (571K) (UPDATED November 15, 2008)
- ``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.
  DOI link: http://dx.doi.org/10.1016/j.ejc.2008.07.009
  - PDF file (176K) (Updated February 2, 2008)
- ``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".)
  - PDF file (202K)
- ``Imprimitive cometric association schemes: constructions and analysis.'' (with Mikhail Muzychuk and Jason Williford). Journal of Algebraic Combinatorics 25 no. 4 (2007), 399--415.
  - PDF file (226K)
  - on-line table of cometric association schemes which are not metric.
- ``A provably secure true random number generator with built-in tolerance to active attacks.'' (with B. Sunar and D.R. Stinson) IEEE Transactions on Computers 56 no. 1 (2007), 109--119.
  - PDF file (212K)
- ``A dual Plotkin bound for (T,M,S)-nets'' (with Terry Visentin) IEEE Trans. Inform. Theory, 53, no. 1 (2007), 411-415..
  - PDF file (241K)
- ``(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 schemes.'' (with Mikhail Muzychuk and Jason Williford). 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).
  - PDF file (183K)
- ``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.
  - PDF file (142K)
- ``A new notion of transitivity for groups and sets of permutations.'' (with B. E. Sagan) Journal of the London Mathematical Society, 73 (2006), 1-13 .
  - Postscript file (144K)
- ``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).
  - Postscript file (158K)
  - PDF file (223K)
- ``A physics-free introduction to quantum error-correcting codes.'' Utilitas Mathematica, 65 (2004), 133-158.
  - PDF file (261K)
- ``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 (2003), 255-271.
  - Postscript file (179K)
- ``Symmetric designs, sets with two intersection numbers, and Krein parameters of incidence graphs'' Journal of Combin. Math. and Combin. Computing 38 (2001), 185-196.
  - Postscript file (138K)
- ``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.
  - Postscript file (198K)
- ``Minimum distance bounds for s-regular codes.'' 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.)
  - Postscript file (134K)
- ``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.
  - Postscript file (300K)
- ``Association schemes for ordered orthogonal arrays and (T,M,S)-nets.'' (with D.R. Stinson), Canad. J. Math. 51, no. 2 (1999), 326-346.
  - Postscript file (363K)
- ``A generalized Rao bound for ordered orthogonal arrays and (t,m,s)-nets.'' (with D.R. Stinson), Canadian Math. Bulletin 42, no. 3 (1999), 359-370.
  - Postscript file (236K)
- ``Designs in product association schemes,'' Designs, Codes, and Crypt. 16, no. 3 (1999), 271-289.
  - Postscript file (416K)
  - PDF file
- ``Completely regular designs,'' J. Combin. Designs 6, no. 4 (1998), 261-273.
  - Postscript file (303K)
- ``Mixed block designs,'' J. Combin. Designs 6, no. 2 (1998), 151-163.
  - Postscript file (340K)
- ``The stipulation polynomial of a uniquely list-colorable graph,'' (with J.H.Dinitz) 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 C.D. Godsil) J. Combin. Th., Ser. A 69, no. 2 (1995), 185-199.
- ``Completely regular designs of strength one,'' J. Alg. Combin. 3 (1994), 177-185.
  - PDF file (283K)
Thesis:
- ``Completely regular subsets'', 1992, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada. Thesis advisor: Chris Godsil.
Unpublished manuscripts:
- "Blind web search: How far are we from a privacy preserving search engine?" (with Gizem Cetin, Wei Dai, Yarkin Doroz and Berk Sunar)
  - Cryptology ePrint Archive: Report 2016/801
- ``The biweight enumerator and the Terwilliger algebra of the hypercube.''
  - PDF file (322K)
  - This project started in 2001 with a talk at the Institute for Advanced Study
- ``On the classification of distance-regular graphs by eigenvalue multiplicity,'' (with R.R. Zhu) -- University of Waterloo Research Report CORR 92-06
- ``Completely regular codes in the Odd graphs.''
Some projects in progress:
- ``Uniform one-factorisations of complete bipartite graphs.'' (with G. Nonay and others)
- Completely regular codes (with Jack Koolen)
- Bounds for codes from the Terwilliger algebra
- Almost orthogonal vectors in Euclidean spaces
- Subconstituent algebras of completely regular codes (with Tara Taylor)
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