THE USES OF FINITE FIELDS
1976) THE USES OF FINITE FIELDS. Technical Report CS76001-R, Computer Science, Virginia Tech. (
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)|
|Deposited By:||Administrator, Eprints|
|Deposited On:||27 April 2006|