The Uses of Finite Fields
| dc.contributor.author | Wesselkamper, Thomas C. | en |
| dc.contributor.department | Computer Science | en |
| dc.date.accessioned | 2013-06-19T14:36:28Z | en |
| dc.date.available | 2013-06-19T14:36:28Z | en |
| dc.date.issued | 1976 | en |
| dc.description.abstract | 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. | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier | http://eprints.cs.vt.edu/archive/00000807/ | en |
| dc.identifier.sourceurl | http://eprints.cs.vt.edu/archive/00000807/01/CS76001-R.pdf | en |
| dc.identifier.trnumber | CS76001-R | en |
| dc.identifier.uri | http://hdl.handle.net/10919/20236 | en |
| dc.language.iso | en | en |
| dc.publisher | Department of Computer Science, Virginia Polytechnic Institute & State University | en |
| dc.relation.ispartof | Historical Collection(Till Dec 2001) | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.title | The Uses of Finite Fields | en |
| dc.type | Technical report | en |
| dc.type.dcmitype | Text | en |
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