**Contemporary Mathematics**

Volume: 518;
2010;
384 pp;
Softcover

MSC: Primary 11; 14; 51; 94;

Print ISBN: 978-0-8218-4786-2

Product Code: CONM/518

List Price: $115.00

Individual Member Price: $92.00

**Electronic ISBN: 978-0-8218-8197-2
Product Code: CONM/518.E**

List Price: $115.00

Individual Member Price: $92.00

# Finite Fields: Theory and Applications

Share this page *Edited by *
*Gary McGuire; Gary L. Mullen; Daniel Panario; Igor E. Shparlinski*

This volume contains the proceedings of the Ninth International Conference
on Finite Fields and Applications, held in Ireland, July 13–17, 2009. It
includes survey papers by all invited speakers as well as selected
contributed papers.

Finite fields continue to grow in mathematical importance due to
applications in many diverse areas. This volume contains a variety of
results advancing the theory of finite fields and connections with, as well
as impact on, various directions in number theory, algebra, and algebraic
geometry. Areas of application include algebraic coding theory, cryptology,
and combinatorial design theory.

#### Readership

Graduate students and research mathematicians interested in finite fields and applications.

# Table of Contents

## Finite Fields: Theory and Applications

- Contents v6 free
- Preface vii8 free
- Construction of new toric quantum codes 110 free
- On the calculation of the linear complexity of periodic sequences 1120
- A few more functions that are not APN infinitely often 2332
- An APN permutation in dimension six 3342
- CCZ-equivalence of single and multi output Boolean functions 4352
- Structural weaknesses of permutations with a low differential uniformity and generalized crooked functions 5564
- Solvability of systems of polynomial equations with some prescribed monomials 7382
- Character sums in finite fields 8392
- Monomial functions with linear structure and permutation polynomials 99108
- Primitive elements on lines in extensions of finite fields 113122
- Commutative semifields of order 243 and 3125 129138
- Normal elliptic bases and torus-based cryptography 137146
- Unitary superperfect binary polynomials 155164
- Shift-invariant polynomials and Ritts Second Theorem 161170
- Waring's problem in finite fields with Dickson polynomials 185194
- Jacobi sums and irreducible polynomials with prescribed trace and restricted norm 193202
- A family of binary sequences from interleaved construction and their cryptographic properties 209218
- Sziklai's conjecture on the number of points of a plane curve over a finite field II 225234
- Folded algebraic-geometric codes from Galois extensions 235244
- A multilinear generalization of the Tate pairing 255264
- The merit factor of binary sequence families constructed from m-sequences 265274
- Intractable problems in cryptography 279288
- Modular curves and coding theory: A survey 301310
- Minimal generating sets of Weierstrass semigroups of certain m-tuples on the norm-trace function field 315324
- On the zeta functions of an optimal tower of function fields over F4 327336
- The asymptotic theory of algebraic-geometry codes 339348
- A spectrum result on maximal partial ovoids of the generalized quadrangle Q(4, q), q odd 349358
- Cyclic codes aspects of bent functions 363372