# Finite Fields: Theory, Applications, and Algorithms

### About this Title

**Gary L. Mullen** and **Peter Jau-Shyong Shiue**, Editors

Publication: Contemporary Mathematics

Publication Year
1994: Volume 168

ISBNs: 978-0-8218-5183-8 (print); 978-0-8218-7759-3 (online)

DOI: http://dx.doi.org/10.1090/conm/168

MathSciNet review: 1291412

### Table of Contents

**Front/Back Matter**

**Articles**

- Pascale Charpin – Tools for coset weight enumerators of some codes [MR 1291413]
- Xuemin Chen, I. S. Reed, T. Helleseth and T. K. Truong – Algebraic decoding of cyclic codes: a polynomial ideal point of view [MR 1291414]
- Stephen D. Cohen – Polynomial factorisation, graphs, designs and codes [MR 1291415]
- Ronald Evans – Character sums as orthogonal eigenfunctions of adjacency operators for Cayley graphs [MR 1291416]
- Michael Fellows and Neal Koblitz – Combinatorial cryptosystems galore! [MR 1291417]
- Raúl Figueroa, Pablo M. Salzberg and Peter Jau-Shyong Shiue – A family of cryptosystems based on combinatorial properties of finite geometries [MR 1291418]
- Michael D. Fried – Global construction of general exceptional covers with motivation for applications to encoding [MR 1291419]
- Shuhong Gao and Joachim von zur Gathen – Berlekamp’s and Niederreiter’s polynomial factorization algorithms [MR 1291420]
- Rainer Göttfert and Harald Niederreiter – Hasse-Teichmüller derivatives and products of linear recurring sequences [MR 1291421]
- S. Gurak – Factors of period polynomials for finite fields. II [MR 1291422]
- Noboru Hamada and Tor Helleseth – A characterization of some ternary codes meeting the Griesmer bound [MR 1291423]
- J. W. P. Hirschfeld and R. Shaw – Projective geometry codes over prime fields [MR 1291424]
- Klaus Huber – Codes over Eisenstein-Jacobi integers [MR 1291425]
- Hubert Kiechle – Points on Fermat curves over finite fields [MR 1291426]
- A. Knopfmacher, J. Knopfmacher and R. Warlimont – Lengths of factorizations for polynomials over a finite field [MR 1291427]
- Jing Hua Kuang – A note on Weil representation of ${\rm SL}_2({\bf F}_q)$ and Soto-Andrade sums [MR 1291428]
- Philippe Langevin – Some sequences with good autocorrelation properties [MR 1291429]
- Hong Wen Lu – Pellian equation conjecture and absolutely nonsingular projective varieties over a finite field—Hecke operator and Pellian equation conjecture. IV [MR 1291430]
- Rex Matthews – Strong pseudoprimes and generalized Carmichael numbers [MR 1291431]
- Oscar Moreno and Victor A. Zinoviev – Transformations of $4$-regular graphs and equations over finite fields of Chevalley-Warning type [MR 1291432]
- Peter Müller – New examples of exceptional polynomials [MR 1291433]
- Harald Niederreiter – New deterministic factorization algorithms for polynomials over finite fields [MR 1291434]
- A. M. Odlyzko – Discrete logarithms and smooth polynomials [MR 1291435]
- Vera Pless – Parents, children, neighbors and the shadow [MR 1291436]
- Ming Hua Qu and S. A. Vanstone – The knapsack problem in cryptography [MR 1291437]
- Alfred Scheerhorn – Iterated constructions of normal bases over finite fields [MR 1291438]
- Lawrence Somer – Periodicity properties of $k$th order linear recurrences whose characteristic polynomial splits completely over a finite field. I [MR 1291439]
- Hong Y. Song and Solomon W. Golomb – Generalized Welch-Costas sequences and their application to Vatican arrays [MR 1291440]
- Stephan J. Suchower – Nonisomorphic complete sets of $F$-rectangles with varying numbers of symbols [MR 1291441]
- Shu Tezuka and Masanori Fushimi – A method of designing cellular automata as pseudorandom number generators for built-in self-test for VLSI [MR 1291442]
- Cynthia E. Trimble – Finite ring sums from $p$-adic $K$-Bessel functions [MR 1291443]
- Paul Thomas Young – On the Gross-Koblitz formula [MR 1291444]
- Jacques Wolfmann – New results on diagonal equations over finite fields from cyclic codes [MR 1291445]
- Gary L. Mullen and Peter Jau-Shyong Shiue – Open Problems and Conjectures