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Self-Reciprocal Irreducible Pentanomials Over \(\mathbb{F}_2\)

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Abstract

Joseph Yucas and Gary Mullen conjectured that there is no self-reciprocal irreducible pentanomial of degree n over \(\mathbb{F}_2\) if n is divisible by 6. In this note we prove this conjecture for the case n ≡ 0, and disprove the conjecture for the case n ≡ 6 (mod 12)

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References

  1. A. J. Menezes, I. F. Blake, X. Gao, R. C. Mullin, S. A. Vanstone and T. Yaghoobian, Applications of Finite Fields, Kluwer (1993).

  2. J.L. Yucas G.L. Mullen (2004) ArticleTitleSelf-reciprocal irreducible polynomials over finite fields Designs Codes and Cryptography 33 IssueID3 275–281 Occurrence Handle10.1023/B:DESI.0000036251.41345.1f Occurrence Handle2005f:11280

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Authors and Affiliations

  1. Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1

    Omran Ahmadi

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  1. Omran Ahmadi
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Correspondence to Omran Ahmadi.

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Communicated by: G. Mullen

AMS Classifications: 11T55

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Ahmadi, O. Self-Reciprocal Irreducible Pentanomials Over \(\mathbb{F}_2\). Des Codes Crypt 38, 395–397 (2006). https://doi.org/10.1007/s10623-005-2031-2

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  • DOI: https://doi.org/10.1007/s10623-005-2031-2

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