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Proceedings of the American Mathematical Society

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Quartics over $ {\rm GF}(2\sp{n})$


Authors: Philip A. Leonard and Kenneth S. Williams
Journal: Proc. Amer. Math. Soc. 36 (1972), 347-350
MSC: Primary 12C05
MathSciNet review: 0308088
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Abstract: A description of the factorization of a quartic polynomial over the field $ {\text{GF}}({2^n})$ is given in terms of the roots of a related cubic.


References [Enhancements On Off] (What's this?)

  • [1] E. R. Berlekamp, H. Rumsey and G. Solomon, Solutions of algebraic equations in fields of characteristic 2, Jet Propulsion Lab. Space Programs Summary 4 (1966), 37-39.
  • [2] E. R. Berlekamp, H. Rumsey, and G. Solomon, On the solution of algebraic equations over finite fields, Information and Control 10 (1967), 553–564. MR 0230706
  • [3] Philip A. Leonard, On factoring quartics (𝑚𝑜𝑑𝑝), J. Number Theory 1 (1969), 113–115. MR 0237469
  • [4] Th. Skolem, The general congruence of the 4th degree modulo 𝑝, 𝑝 prime, Norsk Mat. Tidsskr. 34 (1952), 73–80. MR 0050603

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0308088-6
Keywords: Quartic polynomial, cubic polynomial, factorization, $ {\text{GF}}({2^n})$
Article copyright: © Copyright 1972 American Mathematical Society