G. McGuire

发表

Recurrence matrices and the preservation of dynamical properties

G. McGuire, Nabeel B. Azar, M. Shelhamer, 1997 .

New quasi-symmetric designs constructed using mutually orthogonal Latin squares and Hadamard matrices

Carl Bracken, Gary McGuire, Harold N. Ward, 2006, Des. Codes Cryptogr..

On the Nonlinearity of Exponential Welch Costas Functions

Verónica Requena, Gary McGuire, Konstantinos Drakakis, 2010, IEEE Transactions on Information Theory.

Ternary Kloosterman sums using Stickelberger's theorem and the Gross-Koblitz formula

G. McGuire, F. Gologlu, R. Moloney, 2010, 1005.4548.

A New Angle on Lattice Sieving for the Number Field Sieve

G. McGuire, Oisín Robinson, 2020, 2001.10860.

Weights in codes and genus 2 curves

G. McGuire, J. Voloch, 2003, math/0306060.

A determination of the weight enumerator of the code of the projective plane of order 5

G. McGuire, H. Ward, 1998 .

Z4-linear codes obtained as projections of Kerdock and Delsarte-Goethals codes

A. Calderbank, G. McGuire, 1995 .

Divisibility of L-Polynomials for a Family of Curves

Iv'an Blanco Chac'on, G. McGuire, R. Chapman, 2018, 1801.04189.

Slope Estimates for Generalized Artin-Schreier Curves

Emrah Sercan Yilmaz, G. McGuire, E. Yilmaz, 2016, 1608.08158.

JKL-ECM: an implementation of ECM using Hessian curves

G. McGuire, Oisín Robinson, H. Heer, 2016 .

A simplified setting for discrete logarithms in small characteristic finite fields

Gohar M. M. Kyureghyan, Michael E. Zieve, Sarah E. Anderson, 2015 .

Kasami bent functions are not equivalent to their duals

G. McGuire, G. Leander, P. Langevin, 2007 .

Some results on linearized trinomials that split completely

G. McGuire, D. Mueller, 2019, Finite Fields and their Applications.

Results on Linearized Trinomials having a Certain Rank

G. McGuire, D. Mueller, 2019, 1905.11755.

Quadratic Binomial APN Functions and Absolutely Irreducible Polynomials

G. McGuire, E. Byrne, 2008, 0810.4523.

CM construction of genus 2 curves with p-rank 1

M. Naehrig, G. McGuire, Marco Streng, 2008 .

The Number of Irreducible Polynomials with the First Two Coefficients Fixed over Finite Fields of Odd Characteristic

Emrah Sercan Yilmaz, G. McGuire, E. Yilmaz, 2016, 1609.02314.

Weights in codes and genus 2 curves

G. McGuire, J. Voloch, 2003, math/0306060.

Other Combinatorial Designs

David Coudert, Akihiro Munemasa, Li, 2006 .

Elliptic Curve Cryptography A CM construction for curves of genus 2 with prank 1

M. Naehrig, G. McGuire, Marco Streng, 2011 .

A G ] 2 0 N ov 2 00 8 CM construction of genus 2 curves with prank 1

M. Naehrig, G. McGuire, Marco Streng, 2008 .

The Intersection of Two Fermat Hypersurfaces in P^3 via Computation of Quotient Curves

G. McGuire, Vijaykumar Singh, 2009, 0911.4025.

On The Characteristic Polynomial of Frobenius of Supersingular Abelian Varieties Of Dimension up to 7 over Finite Fields

G. McGuire, Vijaykumar Singh, Alexey Zatysev, 2010, 1005.3635.

Classification of characteristic polynomials of simple supersingular abelian varieties over finite fields

G. McGuire, A. Zaytsev, Vijaykumar Singh, 2014 .

Decomposing Jacobians of curves over finite fields in the absence of algebraic structure

G. McGuire, O. Ahmadi, Antonio Rojas-Le'on, 2014, 1409.8510.

A few more index calculus algorithms for the Elliptic Curve Discrete Logarithm Problem

G. McGuire, D. Mueller, 2018 .

A New Index Calculus Algorithm for the Elliptic Curve Discrete Logarithm Problem and Summation Polynomial Evaluation

G. McGuire, D. Mueller, 2018 .

Primes of the form n^2+n+p have density 1

G. McGuire, Oisín Robinson, I. Blanco-Chacón, 2017, 1707.06014.

On Galois groups of linearized polynomials related to the special linear group of prime degree

G. McGuire, R. Gow, 2022, Linear Algebra and its Applications.

Quantum codes from a new construction of self-orthogonal algebraic geometry codes

G. McGuire, J. Moyano-Fernández, F. Hernando, 2020, Quantum Information Processing.

Characterization of SDP Designs That Yield Certain Spin Models

G. McGuire, Carl Bracken, 2002, Des. Codes Cryptogr..

On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in F21971

Faruk Göloglu, Gary McGuire, Robert Granger, 2013, IACR Cryptol. ePrint Arch..

On the Zeta Functions of an optimal tower of function fields over $\FF_4$

G. McGuire, A. Zaytsev, 2009, 0906.5252.

New families of quadratic almost perfect nonlinear trinomials and multinomials

Eimear Byrne, Carl Bracken, Nadya Markin, 2008, Finite Fields Their Appl..

A few more quadratic APN functions

Eimear Byrne, Carl Bracken, Nadya Markin, 2008, Cryptography and Communications.

A Hardware Analysis of Twisted Edwards Curves for an Elliptic Curve Cryptosystem

William P. Marnane, Gary McGuire, Brian Baldwin, 2009, ARC.

There Is No 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem via Hitting Set Enumeration

Gary McGuire, Gilles Civario, Bastian Tugemann, 2012, Exp. Math..

A bridge over a Hamiltonian path

G. McGuire, F. O. Cairbre, 2001 .

Some congruences of Kloosterman sums and their characteristic polynomials

Gary McGuire, Richard Moloney, Faruk Göloğlu, 2013 .

Some Congruences of Kloosterman Sums and their Minimal Polynomials

Gary McGuire, Richard Moloney, G. McGuire, 2010, 1012.0964.

Ternary Kloosterman Sums Modulo 18 Using Stickelberger's Theorem

Faruk Göloglu, Gary McGuire, Richard Moloney, 2010, SETA.

On the classification of exceptional planar functions over Fp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {

Gary McGuire, Fernando Hernando, Francisco Monserrat, 2013, Geometriae Dedicata.

On the classification of exceptional planar functions over $$\mathbb {F}_{p}$$Fp

Francisco Monserrat, Gary McGuire, Fernando Hernando, 2013, ArXiv.

Two kinds of division polynomials for twisted Edwards curves

Gary McGuire, Richard Moloney, G. McGuire, 2009, Applicable Algebra in Engineering, Communication and Computing.

A characterization of the number of roots of linearized and projective polynomials in the field of coefficients

John Sheekey, Gary McGuire, G. McGuire, 2018, Finite Fields Their Appl..

Divisibility of L-polynomials for a family of Artin–Schreier curves

Emrah Sercan Yilmaz, G. McGuire, 2018, Journal of Pure and Applied Algebra.

Fibre products of supersingular curves and the enumeration of irreducible polynomials with prescribed coefficients

Faruk Göloglu, Gary McGuire, Robert Granger, 2016, Finite Fields Their Appl..

Further results on the number of rational points of hyperelliptic supersingular curves in characteristic 2

Emrah Sercan Yilmaz, G. McGuire, 2015, Des. Codes Cryptogr..

The number of rational points on hyperelliptic supersingular curves of genus 4 in characteristic 2

Alexey Zaytsev, Gary McGuire, G. McGuire, 2012, Finite Fields Their Appl..

A construction of weakly and non-weakly regular bent functions

Wilfried Meidl, Ayça Çesmelioglu, Gary McGuire, 2010, J. Comb. Theory, Ser. A.

Proof of a conjecture of Segre and Bartocci on monomial hyperovals in projective planes

Gary McGuire, Fernando Hernando, G. McGuire, 2010, Des. Codes Cryptogr..

A Counterexample to a Conjecture of Niho

Philippe Langevin, Gregor Leander, Gary McGuire, 2007, IEEE Transactions on Information Theory.

Analysis of Kasami-Welch Functions in Odd Dimension using Stickelberger's Theorem

Philippe Langevin, Gregor Leander, Gary McGuire, 2011 .

Supersingular curves over finite fields and weight divisibility of codes

Cem Güneri, Gary McGuire, G. McGuire, 2014, J. Comput. Appl. Math..

Characterizing the Hermitian and Ree Unitals on 28 Points

Vladimir D. Tonchev, Gary McGuire, Harold N. Ward, 1998, Des. Codes Cryptogr..

Double-Error-Correcting Cyclic Codes and Absolutely Irreducible Polynomials over GF(2)

Heeralal Janwa, Gary McGuire, R. M. Wilson, 1995 .

Solving a 6120 -bit DLP on a Desktop Computer

Faruk Göloglu, Gary McGuire, Robert Granger, 2013, Selected Areas in Cryptography.

On a conjecture of Helleseth regarding pairs of binary m-sequences

A. Robert Calderbank, Gary McGuire, Bjorn Poonen, 1996, IEEE Trans. Inf. Theory.

On Certain 3-Weight Cyclic Codes Having Symmetric Weights and a Conjecture of Helleseth

Gary McGuire, G. McGuire, 2001, SETA.

Construction of Multiblock Space–Time Codes From Division Algebras With Roots of Unity as Nonnorm Elements

Jyrki T. Lahtonen, Nadya Markin, Gary McGuire, 2008, IEEE Transactions on Information Theory.

The weight distributions of cyclic codes with two zeros and zeta functions

Nigel Boston, Gary McGuire, G. McGuire, 2010, J. Symb. Comput..

Curves over finite fields and linear recurring sequences

Gary McGuire, Omran Ahmadi, G. McGuire, 2015, Surveys in Combinatorics.

The Number of Rational Points On Genus 4 Hyperelliptic Supersingular Curves in Characteristic 2

G. McGuire, A. Zaytsev, 2009, 0911.2128.

On the termination of the general XL algorithm and ordinary multinomials

Gary McGuire, Daniela O'Hara, G. McGuire, 2018, J. Symb. Comput..

Construction of bent functions from near-bent functions

Gregor Leander, Gary McGuire, G. McGuire, 2009, J. Comb. Theory, Ser. A.

There Is No 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem via Hitting Set Enumeration

G. McGuire, Bastian Tugemann, G. Civario, 2012, Exp. Math..

On quasi-3 designs and spin models

Carl Bracken, Gary McGuire, G. McGuire, 2005, Discret. Math..

On the non-existence of quasi-3 designs

Gary McGuire, Wayne Broughton, G. McGuire, 2003, Discret. Math..

Some Observations on Quasi-3 Designs and Hadamard Matrices

Gary McGuire, Wayne Broughton, G. McGuire, 1999, Des. Codes Cryptogr..

Characterization of Certain Minimal Rank Designs

Gary McGuire, Harold N. Ward, G. McGuire, 1998, J. Comb. Theory A.

Quasi-Symmetric Designs and Codes Meeting the Grey-Rankin Bound

Gary McGuire, G. McGuire, 1997, J. Comb. Theory A.

Characteristic Polynomial of Supersingular Abelian Varieties over Finite Fields

G. McGuire, A. Zaytsev, Vijaykumar Singh, 2011, 1110.1116.

A CM construction for curves of genus 2 with p-rank 1

Michael Naehrig, Gary McGuire, Laura Hitt O'Connor, 2008, IACR Cryptol. ePrint Arch..

Proof of a Conjecture on the Sequence of Exceptional Numbers, Classifying Cyclic Codes and APN Functions pdf

Gary McGuire, Fernando Hernando, G. McGuire, 2009, ArXiv.

Cyclic codes over Z4, locator polynomials, and Newton's identities

A. Robert Calderbank, Tor Helleseth, P. Vijay Kumar, 1996, IEEE Trans. Inf. Theory.

Quantum codes from a new construction of self-orthogonal algebraic geometry codes

Francisco Monserrat, Gary McGuire, Julio José Moyano-Fernández, 2019, Quantum Inf. Process..

Linearized Polynomials and Their Adjoints, and Some Connections to Linear Sets and Semifields

G. McGuire, John Sheekey, 2020, WAIFI.

On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in $\mathbb{F}_{2^{1971}}$ and $\mathbb{F}_{2^{3164}}$

Gary McGuire, Robert Granger, Jens Zumbrägel, 2013, CRYPTO 2013.

Determining the Nonlinearity of a New Family of APN Functions

Eimear Byrne, Carl Bracken, Nadya Markin, 2007, AAECC.

Subspaces of matrices with special rank properties

John Sheekey, Jean-Guillaume Dumas, Gary McGuire, 2010 .