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Self-Reciprocal Irreducible Polynomials Over Finite Fields

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Abstract

We classify monic self-reciprocal irreducible polynomials over finite fields in terms of their orders. We also study the weights of these polynomials.

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References

  1. I. F. Blake, S. Gao and R. J. Lambert, Construction and distribution problems for irreducible trinomials over finite fields. In D. Gollmann (ed.), Applications of Finite Fields, Clarendon Press, Oxford (1996) pp. 19–32.

    Google Scholar 

  2. K. Cattell, C. R. Miers, F. Ruskey, M. Serra and J. Sawada, The number of irreducible polynomials over GF(2) with given trace and subtrace, J. Comb. Math. Comb. Comp., Vol. 47 (2003) pp. 31–64.

    Google Scholar 

  3. K. H. Hicks, G. L. Mullen and I. Sato, Distribution of irreducible polynomials over finite fields. In G. L. Mullen, H. Stichtenoth and H. Tapia-Recillas (eds.), Finite Fields with Applications in Coding Theory, Cryptography and Related Areas, Springer (2002) pp. 177–186.

  4. S. J. Hong and D. C. Bossen, On some properties of self-reciprocal polynomials, IEEE Trans. Infor. Thy., Vol. IT-21 (1975) pp. 462–464.

    Google Scholar 

  5. D. Jungnickel, Finite Fields, Bibliographisches Institut & F. A. Brockhaus AG, Mannheim (1993).

    Google Scholar 

  6. R. Lidl and H. Niederreiter, Finite Fields, Cambridge Univ. Press, Cambridge (1997).

    Google Scholar 

  7. J. L. Massey, Reversible codes, Information Control, Vol. 7 (1964) pp. 369–380.

    Google Scholar 

  8. H. Meyn, On the construction of irreducible self-reciprocal polynomials over finite fields, Appl. Alg. in Eng., Comm., and Comp., Vol. 1 (1990) pp. 43–53.

    Google Scholar 

  9. R. L. Miller, Necklaces, symmetries and self-reciprocal polynomials,Discrete Math., Vol. 22 (1978) pp. 25–33.

    Google Scholar 

  10. G. L. Mullen and J. Yucas, Irreducible polynomials over GF(2) with prescribed coefficients, preprint.

  11. A. M. Patel and S. J. Hong, Optimal rectangular code for high density magnetic tapes, IBM J. Res. Develop., Vol. 18 (1974) pp. 579–588.

    Google Scholar 

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Authors
  1. Joseph L. Yucas
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  2. Gary L. Mullen
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Yucas, J.L., Mullen, G.L. Self-Reciprocal Irreducible Polynomials Over Finite Fields. Designs, Codes and Cryptography 33, 275–281 (2004). https://doi.org/10.1023/B:DESI.0000036251.41345.1f

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  • DOI: https://doi.org/10.1023/B:DESI.0000036251.41345.1f

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