On the efficiency of algorithms for polynomial factoring

Author:
Robert T. Moenck

Journal:
Math. Comp. **31** (1977), 235-250

MSC:
Primary 12-04; Secondary 68A10, 68A20

DOI:
https://doi.org/10.1090/S0025-5718-1977-0422193-8

MathSciNet review:
0422193

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Abstract | References | Similar Articles | Additional Information

Abstract: Algorithms for factoring polynomials over finite fields are discussed. A construction is shown which reduces the final step of Berlekamp's algorithm to the problem of finding the roots of a polynomial in a finite field .

It is shown that if the characteristic of the field is of the form , where , then the roots of a polynomial of degree *n* may be found in steps.

As a result, a modification of Berlekamp's method can be performed in steps. If *n* is very large then an alternative method finds the factors of the polynomial in . Some consequences and empirical evidence are discussed.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1977-0422193-8

Keywords:
Algebraic manipulation,
polynomial factoring,
roots in finite fields,
analysis of algorithms

Article copyright:
© Copyright 1977
American Mathematical Society