Factoring polynomials over large finite fields
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In this paper, the authors present a deterministic procedure for factoring polynomials over finite fields, which reduces the problem of factoring an arbitrary polynomial over the Galois field GF(p m) to finding the roots in GF(m) of certain other polynomorphisms over GF (m).Abstract:
This paper reviews some of the known algorithms for factoring polynomials over finite fields and presents a new deterministic procedure for reducing the problem of factoring an arbitrary polynomial over the Galois field GF(p m) to the problem of finding the roots in GF(p) of certain other polynomials over GF(p). The amount of computation and the storage space required by these algorithms are algebraic in both the degree of the polynomial to be factored and the logarithm of the order of the finite field. Certain observations on the application of these methods to the factorization of polynomials over the rational integers are also included.read more
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Randomized Algorithms
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References
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Book
Algebraic Coding Theory
TL;DR: This is the revised edition of Berlekamp's famous book, "Algebraic Coding Theory," originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field.
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A survey of modern algebra
TL;DR: In this article, two young instructors who became giants in their field, have shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and text for self study and college courses.
Journal ArticleDOI
Factoring polynomials over finite fields
TL;DR: The method reduces the factorization of a polynomial of degree m over GF(q) to the solution of about m(q − 1)/q linear equations in as many unknowns over GF (q).