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
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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.
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- 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 (Unpublished.)
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Article copyright:
© Copyright 1980
American Mathematical Society