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

- G. McGuire, John Sheekey
- Mathematics, Computer Science
- Finite Fields Their Appl.
- 15 June 2018

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

- F. Hernando, G. McGuire
- Mathematics, Computer Science
- ArXiv
- 11 March 2009

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New families of quadratic almost perfect nonlinear trinomials and multinomials

- C. Bracken, E. Byrne, N. Markin, G. McGuire
- Computer Science, Mathematics
- Finite Fields Their Appl.
- 1 July 2008

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A few more functions that are not APN infinitely often

- Y. Aubry, G. McGuire, Franccois Rodier
- Mathematics
- 12 September 2009

We consider exceptional APN functions on ${\bf F}_{2^m}$, which by definition are functions that are not APN on infinitely many extensions of ${\bf F}_{2^m}$. Our main result is that polynomial… Expand

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

- H. Janwa, G. McGuire, R. M. Wilson
- Mathematics
- 1 December 1995

Codewords of weight ≤ 4 in certain cyclic codes of length n = 2s − 1, parameterized by an odd integer t, can be related to zeros of certain projective plane curves gt(X, Y, Z). Some families of these… Expand

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

- G. McGuire, Bastian Tugemann, G. Civario
- Mathematics, Computer Science
- Exp. Math.
- 1 January 2012

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Construction of bent functions from near-bent functions

- G. Leander, G. McGuire
- Computer Science, Mathematics
- J. Comb. Theory, Ser. A
- 1 May 2009

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

- Faruk Göloğlu, Robert Granger, G. McGuire, J. Zumbrägel
- Mathematics, Computer Science
- IACR Cryptol. ePrint Arch.
- 18 August 2013

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

- G. McGuire
- Mathematics, Computer Science
- J. Comb. Theory, Ser. A
- 1 May 1997

We give a characterization of codes meeting the Grey?Rankin bound. When the codes have even length, the existence of such codes is equivalent to the existence of certain quasi-symmetric designs. We… Expand

On the Nonlinearity of Exponential Welch Costas Functions

- K. Drakakis, V. Requena, G. McGuire
- Computer Science
- IEEE Transactions on Information Theory
- 2010

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