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- Alan G. B. Lauder, Kenneth G. Paterson
- IEEE Trans. Information Theory
- 2003

Binary sequences with high linear complexity are of interest in cryptography. The linear complexity should remain high even when a small number of changes are made to the sequence. The error linear… (More)

- Shuhong Gao, Alan G. B. Lauder
- Discrete & Computational Geometry
- 2001

Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show… (More)

We present a deterministic polynomial time algorithm for computing the zeta function of an arbitrary variety of fixed dimension over a finite field of small characteristic. One consequence of this… (More)

- Fatima Abu Salem, Shuhong Gao, Alan G. B. Lauder
- ISSAC
- 2004

We introduce a new approach to multivariate polynomial factorisation which incorporates ideas from polyhedral geometry, and generalises Hensel lifting. Our main contribution is to present an… (More)

An attractive and challenging problem in computational number theory is to count in an e*cient manner the number of solutions to a multivariate polynomial equation over a -nite -eld. One desires an… (More)

- Alan G. B. Lauder
- Foundations of Computational Mathematics
- 2004

We present a polynomial-time algorithm for computing the zeta function of a smooth projective hypersurface of degree d over a finite field of characteristic p, under the assumption that p is a… (More)

- Richard P. Brent, Shuhong Gao, Alan G. B. Lauder
- SIAM J. Discrete Math.
- 2003

Motivated by a connection with block iterative methods for solving linear systems over finite fields, we consider the probability that the Krylov space generated by a fixed linear mapping and a… (More)

- Emanuel M. Sachs, Michael J. Cima, +8 authors Steve Michaels
- 1993

- Shuhong Gao, Alan G. B. Lauder
- Math. Comput.
- 2002

This paper presents an average time analysis of a Hensel lifting based factorisation algorithm for bivariate polynomials over finite fields. It is shown that the average running time is almost linear… (More)