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Researchers at UCD

Gary McGuire

Full Professor of Mathematics

School of Mathematics & Statistics

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Biography

PhD, Department of Mathematics, California Institute of Technology, 1995.

Professional

Honours and Awards

Year: 2013.
Title: Best Paper Award
                         

Publications

     

Peer Reviewed Journals

Omran Ahmadi, Gary McGuire (2015) 'Decomposing Jacobians of curves over finite fields in the absence of algebraic structure'. Journal of Number Theory, . [DOI] [Details]
Gary McGuire, Emrah Sercan Yilmaz (2015) 'Further results on the number of rational points of hyperelliptic supersingular curves in characteristic 2'. Designs, Codes, and Cryptography, . [DOI] [Details]
Cem Guneri, Gary McGuire (2014) 'Supersingular curves over finite fields and weight divisibility of codes'. Journal of Computational Mathematics, . [DOI] [Details]
Fernando Hernando, Gary McGuire, Francisco Monserrat (2014) 'On the classification of Exceptional Planar Functions over Fp'. Geometriae Dedicata, . [DOI] [Details]
Faruk Gologlu, Gary McGuire (2014) 'On theorems of Carlitz and Payne on permutation polynomials over finite fields with an application to x−1+L(x)'. Finite Fields and their Applications, . [DOI] [Details]
Gologlu, F,McGuire, G,Moloney, R (2013) 'Some congruences of Kloosterman sums and their characteristic polynomials'. Journal of Number Theory, 133 :1596-1607. [DOI] [Details]
McGuire, Gary; Zaytsev, Alexey (2012) 'The number of rational points on hyperelliptic supersingular curves of genus 4 in characteristic 2'. Finite Fields and Their Applications, . [Details]
Gologlu, F,Lisonek, P,McGuire, G,Moloney, R (2012) 'Binary Kloosterman Sums Modulo 256 and Coefficients of the Characteristic Polynomial'. IEEE Transactions on Information Theory, 58 :2516-2523. [DOI] [Details]
Hernando, Fernando; McGuire, Gary (2012) 'Proof of a conjecture of Segre and Bartocci on monomial hyperovals in projective planes'. Designs Codes and Cryptography, . [Details]
Çeşmelioğlu, Ayça; McGuire, Gary; Meidl, Wilfried (2012) 'A construction of weakly and non-weakly regular bent functions'. Journal Of Combinatorial Theory Series A, . [Details]
McGuire, Gary (2012) 'An alternative proof of a result on the weight divisibility of a cyclic code using supersingular curves'. Finite Fields and Their Applications, . [Details]
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]
Moloney, R,McGuire, G (2011) 'Two kinds of division polynomials for twisted Edwards curves'. Applicable Algebra in Engineering, Communications and Computing, 22 :321-345. [DOI] [Details]
Langevin, Philippe; Leander, Gregor; McGuire, Gary; Zălinescu, Eugen (2011) 'Analysis of Kasami-Welch functions in odd dimension using Stickelberger's theorem'. Journal of Combinatorics and Number Theory, . [Details]
Bracken, Carl; Byrne, Eimear; Markin, Nadya; McGuire, Gary (2011) 'A few more quadratic APN functions'. Cryptography and Communications - Discrete Structures, Boolean Functions and Sequences, . [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]
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]
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]
Drakakis, Konstantinos; Gow, Rod; McGuire, Gary (2009) 'APN permutations on Zn and Costas arrays'. Discrete Applied Mathematics, 157 . [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]
Bracken, C,Byrne, E,Markin, N,McGuire, G; (2009) 'Fourier Spectra of Binomial APN Functions'. SIAM Journal of Discrete Mathematics, 23 :596-608. [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]
Dillon, J. F.; McGuire, Gary (2008) 'Near bent functions on a hyperplane'. Finite Fields and Their Applications, . [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]
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]
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]
Bracken, C., Byrne, E., McGuire, G.; (2007) 'On the Walsh Spectrum of a New APN Function'. Lecture Notes in Computer Science, 4887 . [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]
P. Langevin, G. Leander, Gary McGuire; (2007) 'A Counterexample to a Conjecture of Niho'. IEEE TRANSACTIONS ON INFORMATION THEORY, . [Details]
Carl Bracken, Gary McGuire; (2007) 'Duals of quasi-3 designs are not necessarily quasi-3'. Designs, Codes and Cryptography, 44 . [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]
 

Conference Publications

Gologlu, F; Granger, R; McGuire, G; Zumbragel, J (2013) Solving a 6120-bit DLP on a Desktop Computer Selected Areas in Cryptography [Details]
Aubry, Yves; McGuire, Gary; Rodier, François (2010) A few more functions that are not APN infinitely often 9th International Conference on Finite Fields and Applications [Details]
McGuire, Gary; Zaytsev, Alexey (2010) On the zeta functions of an optimal tower of function fields over F4 9th International Conference on Finite Fields and Applications [Details]
Langevin, Philippe; Leander, Gregor; McGuire, Gary (2008) Kasami bent functions are not equivalent to their duals 8th International Conference on Finite Fields and Applications [Details]
   

Editorial

Arasu, KT,Liu, XY,McGuire, G (2012) Preface: Richard M. Wilson, Special issue honoring his 65th birthday. Editorial [DOI] [Details]
                                                                                                           

Research

Research Interests

Discrete Mathematics, Error Correction, Cryptography, Computation, Algebra, Number Theory, Algebraic Geometry.

Research Projects

Sponsor : Irish Research Council (IRC)
Title : Finite Semirings and DLP Based Cryptosystems
Start Date / End Date : 01-OCT-13 / 30-SEP-16
Sponsor : Science Foundation Ireland (SFI)
Title : The invariants of abelian varieties with complex multiplication and the CM lifting
Start Date / End Date : 01-NOV-09 / 31-DEC-10
Sponsor : Irish Research Council for Science Engineering and Technology (IRCSET)
Title : Subfield-Subcodes and Algebraic Geometry codes
Start Date / End Date : 16-AUG-10 / 31-JAN-13
Sponsor : Enterprise Ireland (EI)
Title : Design of Secure Encryption for Logscreen
Start Date / End Date : 01-JUL-10 / 31-DEC-10
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 / 31-JUL-13
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

Recent Postgraduates

Richard Moloney
Vijaykumar Singh
Carl Bracken