Proof of a conjecture of Sarwate and Pursley regarding pairs of binary m-sequences. - Gary McGuire; A. Robert Calderbank (IEEE Trans. Inf. Theory, 1995)

Cyclic codes over Z4, locator polynomials, and Newton's identities. - A. Robert Calderbank; Gary McGuire; P. Vijay Kumar; Tor Helleseth (IEEE Trans. Inf. Theory, 1996)

On a conjecture of Helleseth regarding pairs of binary m-sequences. - A. Robert Calderbank; Gary McGuire; Bjorn Poonen; Michael Rubinstein (IEEE Trans. Inf. Theory, 1996)

Construction of a (64, 237, 12) Code via Galois Rings. - A. Robert Calderbank; Gary McGuire (Des. Codes Cryptogr., 1997)

Quasi-Symmetric Designs and Codes Meeting the Grey-Rankin Bound. - Gary McGuire (J. Comb. Theory A, 1997)

Characterizing the Hermitian and Ree Unitals on 28 Points. - Gary McGuire; Vladimir D. Tonchev; Harold N. Ward (Des. Codes Cryptogr., 1998)

Characterization of Certain Minimal Rank Designs. - Gary McGuire; Harold N. Ward (J. Comb. Theory A, 1998)

Some Observations on Quasi-3 Designs and Hadamard Matrices. - Wayne Broughton; Gary McGuire (Des. Codes Cryptogr., 1999)

On Certain 3-Weight Cyclic Codes Having Symmetric Weights and a Conjecture of Helleseth. - Gary McGuire (SETA, 2001)

On the non-existence of quasi-3 designs. - Wayne Broughton; Gary McGuire (Discret. Math., 2003)

On three weights in cyclic codes with two zeros. - Gary McGuire (Finite Fields Their Appl., 2004)

Characterization of SDP Designs That Yield Certain Spin Models. - Carl Bracken; Gary McGuire (Des. Codes Cryptogr., 2005)

On quasi-3 designs and spin models. - Carl Bracken; Gary McGuire (Discret. Math., 2005)

New quasi-symmetric designs constructed using mutually orthogonal Latin squares and Hadamard matrices. - Carl Bracken; Gary McGuire; Harold N. Ward (Des. Codes Cryptogr., 2006)

Determining the Nonlinearity of a New Family of APN Functions. - Carl Bracken; Eimear Byrne; Nadya Markin; Gary McGuire (AAECC, 2007)

Spectra of Boolean Functions, Subspaces of Matrices, and Going Up Versus Going Down. - Gary McGuire (AAECC, 2007)

On the Walsh Spectrum of a New APN Function. - Carl Bracken; Eimear Byrne; Nadya Markin; Gary McGuire (IMACC, 2007)

Gold and Kasami-Welch functions, quadratic forms, and bent functions. - Jyrki T. Lahtonen; Gary McGuire; Harold N. Ward (Adv. Math. Commun., 2007)

Duals of quasi-3 designs are not necessarily quasi-3. - Carl Bracken; Gary McGuire (Des. Codes Cryptogr., 2007)

Quadratic Almost Perfect Nonlinear Functions With Many Terms. - Carl Bracken; Eimear Byrne; Nadya Markin; Gary McGuire (IACR Cryptol. ePrint Arch., 2007)

A Counterexample to a Conjecture of Niho. - Philippe Langevin; Gregor Leander; Gary McGuire (IEEE Trans. Inf. Theory, 2007)

New families of quadratic almost perfect nonlinear trinomials and multinomials. - Carl Bracken; Eimear Byrne; Nadya Markin; Gary McGuire (Finite Fields Their Appl., 2008)

Near bent functions on a hyperplane. - J. F. Dillon; Gary McGuire (Finite Fields Their Appl., 2008)

A CM construction for curves of genus 2 with p-rank 1. - Laura Hitt O'Connor; Gary McGuire; Michael Naehrig; Marco Streng (IACR Cryptol. ePrint Arch., 2008)

Construction of Multiblock Space-Time Codes From Division Algebras With Roots of Unity as Nonnorm Elements. - Jyrki T. Lahtonen; Nadya Markin; Gary McGuire (IEEE Trans. Inf. Theory, 2008)

Proof of a Conjecture on the Sequence of Exceptional Numbers, Classifying Cyclic Codes and APN Functions - Fernando Hernando; Gary McGuire (CoRR, 2009)

APN permutations on Zn and Costas arrays. - Konstantinos Drakakis; Rod Gow; Gary McGuire (Discret. Appl. Math., 2009)

A Hardware Analysis of Twisted Edwards Curves for an Elliptic Curve Cryptosystem. - Brian Baldwin; Richard Moloney; Andrew Byrne; Gary McGuire; William P. Marnane (IACR Cryptol. ePrint Arch., 2009)

Elliptic Curves in Montgomery Form with B=1 and Their Low Order Torsion. - Richard Moloney; Gary McGuire; Michael Markowitz (IACR Cryptol. ePrint Arch., 2009)

Construction of bent functions from near-bent functions. - Gregor Leander; Gary McGuire (J. Comb. Theory A, 2009)

Fourier Spectra of Binomial APN Functions. - Carl Bracken; Eimear Byrne; Nadya Markin; Gary McGuire (SIAM J. Discret. Math., 2009)

S-Boxes, APN Functions and Related Codes. - Rafael Álvarez; Gary McGuire (Enhancing Cryptographic Primitives with Techniques from Error Correcting Codes, 2009)

Ternary Kloosterman Sums Modulo 18 Using Stickelberger's Theorem. - Faruk Göloglu; Gary McGuire; Richard Moloney (SETA, 2010)

The weight distributions of cyclic codes with two zeros and zeta functions. - Nigel Boston; Gary McGuire (J. Symb. Comput., 2010)

On the nonlinearity of exponential welch costas functions. - Konstantinos Drakakis; Verónica Requena; Gary McGuire (IEEE Trans. Inf. Theory, 2010)

Two kinds of division polynomials for twisted Edwards curves. - Richard Moloney; Gary McGuire (Appl. Algebra Eng. Commun. Comput., 2011)

A few more quadratic APN functions. - Carl Bracken; Eimear Byrne; Nadya Markin; Gary McGuire (Cryptogr. Commun., 2011)

On the equivalence of quadratic APN functions. - Carl Bracken; Eimear Byrne; Gary McGuire; Gabriele Nebe (Des. Codes Cryptogr., 2011)

There is no 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem - Gary McGuire; Bastian Tugemann; Gilles Civario (CoRR, 2012)

Preface: Richard M. Wilson, Special issue honoring his 65th birthday. - K. T. Arasu 001; Xiaoyu Liu 009; Gary McGuire (Des. Codes Cryptogr., 2012)

Proof of a conjecture of Segre and Bartocci on monomial hyperovals in projective planes. - Fernando Hernando; Gary McGuire (Des. Codes Cryptogr., 2012)

An alternative proof of a result on the weight divisibility of a cyclic code using supersingular curves. - Gary McGuire (Finite Fields Their Appl., 2012)

The number of rational points on hyperelliptic supersingular curves of genus 4 in characteristic 2. - Gary McGuire; Alexey Zaytsev 001 (Finite Fields Their Appl., 2012)

A construction of weakly and non-weakly regular bent functions. - Ayça Çesmelioglu; Gary McGuire; Wilfried Meidl (J. Comb. Theory A, 2012)

Binary Kloosterman Sums Modulo 256 and Coefficients of the Characteristic Polynomial. - Faruk Göloglu; Petr Lisonek; Gary McGuire; Richard Moloney (IEEE Trans. Inf. Theory, 2012)

Finite field transforms. - Gary McGuire (Handbook of Finite Fields, 2013)

On The Classification of Perfect Nonlinear (PN) and Almost Perfect Nonlinear (APN) Monomial Functions. - Fernando Hernando; Gary McGuire (Finite Fields and Their Applications, 2013)

On the Function Field Sieve and the Impact of Higher Splitting Probabilities - Application to Discrete Logarithms in and. - Faruk Göloglu; Robert Granger; Gary McGuire; Jens Zumbrägel (CRYPTO (2), 2013)

On the Classification of Exceptional Planar Functions over $ mathbb{F}_{p}$ - Fernando Hernando; Gary McGuire; Francisco Monserrat (CoRR, 2013)

On the Function Field Sieve and the Impact of Higher Splitting Probabilities: Application to Discrete Logarithms in F21971. - Faruk Göloglu; Robert Granger; Gary McGuire; Jens Zumbrägel (IACR Cryptol. ePrint Arch., 2013)

Solving a 6120-bit DLP on a Desktop Computer. - Faruk Göloglu; Robert Granger; Gary McGuire; Jens Zumbrägel (IACR Cryptol. ePrint Arch., 2013)

There Is No 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem via Hitting Set Enumeration. - Gary McGuire; Bastian Tugemann; Gilles Civario (Exp. Math., 2014)

On theorems of Carlitz and Payne on permutation polynomials over finite fields with an application to x-1+L(x). - Faruk Göloglu; Gary McGuire (Finite Fields Their Appl., 2014)

Supersingular curves over finite fields and weight divisibility of codes. - Cem Güneri; Gary McGuire (J. Comput. Appl. Math., 2014)

Curves over finite fields and linear recurring sequences. - Omran Ahmadi; Gary McGuire (Surveys in Combinatorics, 2015)

Further results on the number of rational points of hyperelliptic supersingular curves in characteristic 2. - Gary McGuire; Emrah Sercan Yilmaz (Des. Codes Cryptogr., 2015)

Fibre products of supersingular curves and the enumeration of irreducible polynomials with prescribed coefficients. - Omran Ahmadi; Faruk Göloglu; Robert Granger; Gary McGuire; Emrah Sercan Yilmaz (Finite Fields Their Appl., 2016)

JKL-ECM: an implementation of ECM using Hessian curves. - Henriette Heer; Gary McGuire; Oisín Robinson (LMS J. Comput. Math., 2016)

A few more index calculus algorithms for the ECDLP. - Gary McGuire; Daniela Müller (IACR Cryptol. ePrint Arch., 2017)

On the zeta functions of supersingular curves. - Gary McGuire; Emrah Sercan Yilmaz (Finite Fields Their Appl., 2018)

A characterization of the number of roots of linearized and projective polynomials in the field of coefficients. - Gary McGuire; John Sheekey (Finite Fields Their Appl., 2019)

Linearized Polynomials and Their Adjoints, and Some Connections to Linear Sets and Semifields. - Gary McGuire; John Sheekey (WAIFI, 2020)

Quantum codes from a new construction of self-orthogonal algebraic geometry codes. - Fernando Hernando; Gary McGuire; Francisco Monserrat; Julio José Moyano-Fernández (Quantum Inf. Process., 2020)

Lattice Sieving in Three Dimensions for Discrete Log in Medium Characteristic. - Gary McGuire; Oisín Robinson (J. Math. Cryptol., 2021)

On the termination of the general XL algorithm and ordinary multinomials. - Gary McGuire; Daniela O'Hara (J. Symb. Comput., 2021)

Decoding Algorithm for Quadruple-Error-Correcting Reed-Solomon Codes and Its Derived Architectures. - Francisco Garcia-Herrero; Gary McGuire; Mark F. Flanagan; Alfonso Sánchez-Macián; Juan Antonio Maestro (IEEE Trans. Circuits Syst. II Express Briefs, 2021)

Invariant rational functions, linear fractional transformations and irreducible polynomials over finite fields. - Rod Gow; Gary McGuire (Finite Fields Their Appl., 2022)

MDS, Hermitian almost MDS, and Gilbert-Varshamov quantum codes from generalized monomial-Cartesian codes. - Beatriz Barbero-Lucas; Fernando Hernando; Helena Martín-Cruz; Gary McGuire (Quantum Inf. Process., 2024)

New Quantum MDS Codes with Flexible Parameters from Hermitian Self-Orthogonal GRS Codes. - Oisin Campion; Fernando Hernando; Gary McGuire (CoRR, 2025)