Includes bibliographical references.

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

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

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