eBook ISBN:  9780821877593 
Product Code:  CONM/168.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821877593 
Product Code:  CONM/168.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 168; 1994; 402 ppMSC: Primary 11; Secondary 05; 94
Because of their applications in so many diverse areas, finite fields continue to play increasingly important roles in various branches of modern mathematics, including number theory, algebra, and algebraic geometry, as well as in computer science, information theory, statistics, and engineering. Computational and algorithmic aspects of finite field problems also continue to grow in importance. This volume contains the refereed proceedings of a conference entitled Finite Fields: Theory, Applications and Algorithms, held in August 1993 at the University of Nevada at Las Vegas. Among the topics treated are theoretical aspects of finite fields, coding theory, cryptology, combinatorial design theory, and algorithms related to finite fields. Also included is a list of open problems and conjectures. This volume is an excellent reference for applied and research mathematicians as well as specialists and graduate students in information theory, computer science, and electrical engineering.
ReadershipGraduate students and researchers in the theory and application of finite fields. More generally, students and researchers in algebra, number theory, combinatorial design theory, coding theory, and cryptology.

Table of Contents

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 JauShyong 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 — HasseTeichmüller 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 EisensteinJacobi 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 SotoAndrade 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 ChevalleyWarning 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 WelchCostas 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 builtin selftest for VLSI [ MR 1291442 ]

Cynthia E. Trimble — Finite ring sums from $p$adic $K$Bessel functions [ MR 1291443 ]

Paul Thomas Young — On the GrossKoblitz formula [ MR 1291444 ]

Jacques Wolfmann — New results on diagonal equations over finite fields from cyclic codes [ MR 1291445 ]

Gary L. Mullen and Peter JauShyong Shiue — Open Problems and Conjectures


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Because of their applications in so many diverse areas, finite fields continue to play increasingly important roles in various branches of modern mathematics, including number theory, algebra, and algebraic geometry, as well as in computer science, information theory, statistics, and engineering. Computational and algorithmic aspects of finite field problems also continue to grow in importance. This volume contains the refereed proceedings of a conference entitled Finite Fields: Theory, Applications and Algorithms, held in August 1993 at the University of Nevada at Las Vegas. Among the topics treated are theoretical aspects of finite fields, coding theory, cryptology, combinatorial design theory, and algorithms related to finite fields. Also included is a list of open problems and conjectures. This volume is an excellent reference for applied and research mathematicians as well as specialists and graduate students in information theory, computer science, and electrical engineering.
Graduate students and researchers in the theory and application of finite fields. More generally, students and researchers in algebra, number theory, combinatorial design theory, coding theory, and cryptology.

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 JauShyong 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 — HasseTeichmüller 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 EisensteinJacobi 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 SotoAndrade 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 ChevalleyWarning 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 WelchCostas 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 builtin selftest for VLSI [ MR 1291442 ]

Cynthia E. Trimble — Finite ring sums from $p$adic $K$Bessel functions [ MR 1291443 ]

Paul Thomas Young — On the GrossKoblitz formula [ MR 1291444 ]

Jacques Wolfmann — New results on diagonal equations over finite fields from cyclic codes [ MR 1291445 ]

Gary L. Mullen and Peter JauShyong Shiue — Open Problems and Conjectures