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Introduction

The Galois fields of characteristic 2 have been widely used in technological applications, mainly in Coding Theory and Cryptography. Each Galois field of characteristic 2, let us say of degree $n$, has as cardinality the corresponding power of 2, and its elements are representable by $n$-degree polynomials, thus the Galois field can be identified with the set of integers with extrems 0 and $2^n-1$. In this document we translate the operations in the Galois field into that integer interval and we plot as density graphs the translated operations, just to give a global glimpse of the field operations. All graphs were obtained using Mathematica 3.0. All concepts mentioned here can be explored more deeply in the classical text of Lidl and Niederreiter [1].



Guillermo M. Luna
2010-02-19