Computer Science Technical Reports
CS at VT


Wesselkamper, T. C. (1976) THE USES OF FINITE FIELDS. Technical Report CS76001-R, Computer Science, Virginia Tech.

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The paper is tutorial in nature, although some of the results are new. It reviews some of the elementary facts about the structure and construction of finite fields and hypothesizes a computer whose fundamental instruction set consists of the Galois field operations. Each total function is shown to be defined by a unique polynomial and this normal representation is also the minimal polynomial representation. A method is presented, due to Newton, for constructing the coefficients of the defining polynomial using divided differences. It is shown that under certain circumstances a total function may be more efficiently evaluated by a rational form with non-zero denominator. Finally a rational form representation is shown to be a natural representation for each partial function. In the light of these considerations the process of producing code for the hypothetical machine is almost entirely automated.

Item Type:Departmental Technical Report
Subjects:Computer Science > Historical Collection(Till Dec 2001)
ID Code:807
Deposited By:Administrator, Eprints
Deposited On:27 April 2006