Professor Gary McGuire BSc MSc PhD
Contact Details
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Biography:
| PhD, Department of Mathematics, California Institute of Technology, 1995. |
Research Interests
| Error Correction, Cryptography, Discrete Mathematics, Algebra, Number Theory, Algebraic Geometry. |
Research Projects
| Sponsor : Science Foundation Ireland (SFI) Title : About Decoding Quasi Cyclic Codes Start Date / End Date : 07-NOV-08 / 22-NOV-08 |
| Sponsor : Irish Research Council for Science Engineering and Technology (IRCSET) Title : Elliptic and Hyper elliptic Curve Cryptography and Genus 2 Curves Start Date / End Date : 01-SEP-07 / 31-AUG-10 |
| Sponsor : Science Foundation Ireland (SFI) Title : Genus 2 Curves and their applications to Cryptography and coding theory Start Date / End Date : 01-SEP-07 / 31-AUG-10 |
| Sponsor : Science Foundation Ireland (SFI) Title : Claude Shannon Institute for Discrete Mathematics, coding and crytography Start Date / End Date : 01-JUL-06 / 30-JUN-12 |
| Sponsor : University College Dublin (UCD) Title : Application for funding for the 9th International Conference on Finite Fields and their Applications, which is being hosted by the Claude Shannon Institute, to be held at UCD on July 13-17 2009. Start Date / End Date : 01-JAN-09 / 30-JUN-10 |
Peer Reviewed Journals
| E. Byrne, C. Bracken, G. McGuire, G. Nebe; (2011) 'On the Equivalence of Quadratic APN Functions'. Designs Codes and Cryptography, 61 (3):261-272. [DOI] [Details] |
| Hernando, F,McGuire, G; (2011) 'Proof of a conjecture on the sequence of exceptional numbers, classifying cyclic codes and APN functions'. Journal of Algebra, 343 :78-92. [DOI] [Details] |
| Gologlu, F,McGuire, G,Moloney, R; (2011) 'Binary Kloosterman sums using Stickelberger's theorem and the Gross-Koblitz formula'. Acta Arithmetica, 148 :269-279. [DOI] [Details] |
| O'Connor, LH,McGuire, G,Naehrig, M,Streng, M; (2011) 'A CM construction for curves of genus 2 with p-rank 1'. Journal of Number Theory, 131 :920-935. [DOI] [Details] |
| Dumas, JG,Gow, R,McGuire, G,Sheekey, J; (2010) 'Subspaces of matrices with special rank properties'. Linear Algebra and Its Applications, 433 :191-202. [DOI] [Details] |
| Boston, N,McGuire, G; (2010) 'The weight distributions of cyclic codes with two zeros and zeta functions'. Journal of Symbolic Computation, 45 :723-733. [DOI] [Details] | |||||||||
| Drakakis, K,Requena, V,McGuire, G; (2010) 'On the Nonlinearity of Exponential Welch Costas Functions'. IEEE Transactions on Information Theory, 56 :1230-1238. [DOI] [Details] | |||||||||
| McGuire, G,Ward, HN; (2009) 'Cocyclic Hadamard matrices from forms over finite Frobenius rings'. Linear Algebra and Its Applications, 430 :1730-1738. [DOI] [Details] | |||||||||
| Bracken, C,Byrne, E,Markin, N,McGuire, G; (2009) 'FOURIER SPECTRA OF BINOMIAL APN FUNCTIONS'. math, 23 :596-608. [DOI] [Details] | |||||||||
| Leander, G,McGuire, G; (2009) 'Construction of bent functions from near-bent functions'. Journal Of Combinatorial Theory Series A, 116 :960-970. [DOI] [Details] | |||||||||
| Drakakis, K,Gow, R,McGuire, G; (2009) 'APN permutations on Z(n) and Costas arrays'. math, 157 :3320-3326. [DOI] [Details] | |||||||||
| Lahtonen, J,Markin, N,McGuire, G; (2008) 'Construction of Multiblock Space-Time Codes From Division Algebras With Roots of Unity as Nonnorm Elements'. IEEE Transactions on Information Theory, 54 :5231-5235. [DOI] [Details] | |||||||||
| Bracken, C,Byrne, E,Markin, N,McGuire, G; (2008) 'New families of quadratic almost perfect nonlinear trinomials and multinomials'. Finite Fields and Their Applications, 14 :703-714. [DOI] [Details] | |||||||||
| P. Langevin, G. Leander, Gary McGuire; (2007) 'A Counterexample to a Conjecture of Niho'. IEEE TRANSACTIONS ON INFORMATION THEORY, . [Details] | |||||||||
| Lahtonen, J,McGuire, G,Ward, HN; (2007) 'Gold and Kasami-Welch functions, quadratic forms, and bent functions'. math, 1 :243-250. [Details] | |||||||||
| Bracken, C,McGuire, G; (2007) 'Duals of quasi-3 designs are not necessarily quasi-3'. DESIGN CODE CRYPTOGR, 44 :157-167. [DOI] [Details] | |||||||||
| Langevin, P,Leander, G,McGuire, G; (2007) 'A counterexample to a conjecture of Niho'. IEEE Transactions on Information Theory, 53 :4785-4786. [DOI] [Details] | |||||||||
| Lahtonen, J., McGuire, G., Ward, H. N., ; (2007) 'Gold and Kasami-Welch functions, quadratic forms, and bent functions'. Advances in Mathematics of Communications, 1 (2):243-250. [Details] | |||||||||
| Bracken, C., Byrne, E., McGuire, G.; (2007) 'On the Walsh Spectrum of a New APN Function'. Lecture Notes in Computer Science, 4887 . [Details] | |||||||||
| Langevin, P., Leander, G., McGuire, G., ; (2007) 'A counterexample to a conjecture of Niho'. IEEE Transactions on Information Theory, 53 (12):4785-4786. [Details] | |||||||||
| Carl Bracken, Gary McGuire; (2007) 'Duals of quasi-3 designs are not necessarily quasi-3'. Designs, Codes and Cryptography, 44 . [Details] | |||||||||
| Jyrki Lahtonen, Gary McGuire, Harold Ward; (2007) 'Gold and Kasami-Welch Functions, Quadratic Forms, and Bent Functions'. Advances in Mathematics of Communications, 1 (2). [Details] | |||||||||
| Marcus Greferath, Gary McGuire, Michael E. O'Sullivan; (2006) 'Plotkin-Optimal Codes over Finite Frobenius Rings'. Journal of Algebra and its Applications, 5 . [Details] | |||||||||
| Carl Bracken, Gary McGuire and Harold Ward; (2006) 'New Quasi-Symmetric Designs Constructed using Mutually Orthogonal Latin Squares and Hadamard Matrices'. Designs, Codes and Cryptography, 41 . [Details] | |||||||||
| Gary McGuire and Jose Felipe Voloch; (2005) 'Weights in Codes and Genus 2 Curves'. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 133 (8). [Details] | |||||||||
| Carl Bracken and Gary McGuire; (2005) 'Characterization of SDP Designs that yield certain Spin Models'. Designs, Codes and Cryptography, 36 . [Details] | |||||||||
| Carl Bracken and Gary McGuire; (2005) 'On Quasi-3 Designs and Spin Models'. DISCRETE MATHEMATICS, 294 . [Details] | |||||||||
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Teaching Interests
Recent Postgraduates
Current Postgraduate Students
| David Conti, Doctor of Philosophy (PhD) - Thesis Supervisor |
Modules Taught
| 201100 MATH10190 Mathematics: How to Solve it |
| 201100 MATH30250 Mathematics: Cryptography: Theory & Practic |
| 201000 MATH30250 Mathematics: Cryptography: Theory & Practic |
| 201000 MATH10190 Mathematics: How to Solve it |
| 200900 MATH10190 Mathematics: How to Solve it |