Factorization of polynomials over finite fields
Robert J. McEliece
Math. Comp. 23 (1969), 861-867
Primary 12.25; Secondary 94.00
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Abstract: If is a polynomial over , we observe (as has Berlekamp) that if , then . The object of this paper is to give an explicit construction of enough such 's so that the repeated application of this result will succeed in separating all irreducible factors of . The 's chosen are loosely defined by . A detailed example over is given, and a table of the factors of the cyclotomic polynomials , is included.
R. W. Marsh, Table of Irreducible Polynomials over through Degree 19, NSA, U.S. Department of Commerce, Office of Tech. Service, Washington, D.C., 1951.
R. Berlekamp, Factoring polynomials over finite fields, Bell
System Tech. J. 46 (1967), 1853–1859. MR 0219231
Lang, Algebra, Addison-Wesley Publishing Co., Inc., Reading,
Mass., 1965. MR
0197234 (33 #5416)
- R. W. Marsh, Table of Irreducible Polynomials over through Degree 19, NSA, U.S. Department of Commerce, Office of Tech. Service, Washington, D.C., 1951.
- E. R. Berlekamp, ``Factoring polynomials over finite fields,'' Bell System Tech. J., v. 46, 1967, pp. 1853-1859. MR 36 #2314. MR 0219231 (36:2314)
- S. Lang, Algebra, Addison-Wesley, Reading, Mass., 1965. MR 33 #5416. MR 0197234 (33:5416)
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