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 | 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.

**[1]**N. ABRAMSON,*Information Theory and Coding*, McGraw-Hill, New York, 1963. MR**0189890 (32:7308)****[2]**T. C. BARTEE & D. I. SCHNEIDER, "Computation with finite fields,"*Inform. and Control.*, v. 6, 1963, pp. 79-98. MR**0162656 (28:5854)****[3]**J. T. B. BEARD, "Computing in ,"*Math. Comp.*, v. 28, 1974, pp. 1159-1168. MR**0352058 (50:4546)****[4]**H. DAVENPORT, "Bases for finite fields,"*J. London Math. Soc.*, v. 43, 1968, pp. 21-39. MR**0227144 (37:2729)****[5]**W. W. PETERSON & E. J. WELDON, Jr.,*Error-Correcting Codes*, 2nd ed., M.I.T. Press, Cambridge, Mass., 1972. MR**0347444 (49:12164)****[6]**G. R. REDINBO,*Finite Field Arithmetic on an Array Processor*, Electrical and Systems Engineering Department, Rensselaer Polytechnic Institute. (Unpublished.)

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DOI:
https://doi.org/10.1090/S0025-5718-1980-0583513-7

Article copyright:
© Copyright 1980
American Mathematical Society