Arithmetic in a finite field
Author:
Michael Willett
Journal:
Math. Comp. 35 (1980), 1353-1359
MSC:
Primary 12-04; Secondary 68C20
DOI:
https://doi.org/10.1090/S0025-5718-1980-0583513-7
MathSciNet review:
583513
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: An algorithm for realizing finite field arithmetic is presented. The relationship between linear recursions and polynomial arithmetic (modulo a fixed polynomial) over Zp is exploited to reduce the storage and computation requirements of the algorithm. A primitive normal polynomial is used to simplify the calculation of multiplicative inverses.
- Norman Abramson, Informantion theory and coding, McGraw-Hill Book Co., New York-Toronto-London, 1963. MR 0189890
- Thomas C. Bartee and David I. Schneider, Computation with finite fields, Information and Control 6 (1963), 79β98. MR 162656
- Jacob T. B. Beard Jr., Computing in ${\rm GF}\,(q)$, Math. Comp. 28 (1974), 1159β1166. MR 352058, DOI https://doi.org/10.1090/S0025-5718-1974-0352058-9
- H. Davenport, Bases for finite fields, J. London Math. Soc. 43 (1968), 21β39. MR 227144, DOI https://doi.org/10.1112/jlms/s1-43.1.21
- W. Wesley Peterson and E. J. Weldon Jr., Error-correcting codes, 2nd ed., The M.I.T. Press, Cambridge, Mass.-London, 1972. MR 0347444 G. R. REDINBO, Finite Field Arithmetic on an Array Processor, Electrical and Systems Engineering Department, Rensselaer Polytechnic Institute. (Unpublished.)
Retrieve articles in Mathematics of Computation with MSC: 12-04, 68C20
Retrieve articles in all journals with MSC: 12-04, 68C20
Additional Information
Article copyright:
© Copyright 1980
American Mathematical Society
