ACAC Seminar Abstract

ACAC Seminar Abstract

ACAC Seminars

ACAC Seminar Abstract

Some Applications of Character Sums

Speaker: Arne Winterhof
Date, Time: Fri, 24 Feb 2012 09:30

Character sums are important tools in the theory of finite fields since they govern the hidden relation between the additive and multiplicative structure of the Field.

In this talk we mention some applications of character sums including check digit systems (e.g. ISBN and IBAN) and pseudorandom numbers. For the construction of check digit systems which cannot detect only single errors but also neighbor transpositions (ab -> ba) orthomorphisms are pertinent, i.e., permutation polynomials f(X) of a finite field such that f(X) - X is also a permutation polynomial. Orthomorphisms can be constructed using multiplicative characters and their number can be estimated with character sums.

The integration error for the Monte-Carlo integration depends on the distribution of the used pseudorandom numbers. Their quality can be evaluated via additive character sums.

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