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Linearized Polynomials and Their Adjoints, and Some Connections to Linear Sets and Semifields

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Arithmetic of Finite Fields (WAIFI 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12542))

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Abstract

Throughout this paper we let p be a prime number, let \(q=p^r\) and let \(\mathbb {F}_{q^n}\) denote a finite field with \(q^n\) elements, where n is a positive integer.

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References

  1. Ball, S., Ebert, G., Lavrauw, M.: A geometric construction of finite semifields. J. Algebra 311, 117–129 (2007)

    Article  MathSciNet  Google Scholar 

  2. Bartoli, D., Giulietti, M., Marino, G., Polverino, O.: Maximum scattered linear sets and complete caps in Galois spaces. Combinatorica 38, 255–278 (2018)

    Article  MathSciNet  Google Scholar 

  3. Csajbók, B., Marino, G., Polverino, O.: A Carlitz type result for linearized polynomials. Ars Math. Contemp. 16(2), 585–608 (2019)

    Article  MathSciNet  Google Scholar 

  4. Csajbók, B., Marino, G., Polverino, O.: Classes and equivalence of linear sets in PG\((1, q^n)\). J. Comb. Theory Ser. A 157, 402–426 (2018)

    Article  Google Scholar 

  5. Csajbók, B., Zanella, C.: On the equivalence of linear sets. Des. Codes Cryptogr. 81, 269–281 (2016)

    Article  MathSciNet  Google Scholar 

  6. Lavrauw, M., Sheekey, J.: The BEL-rank of finite semifields. Des. Codes Cryptogr. 84, 345–358 (2017)

    Article  MathSciNet  Google Scholar 

  7. Sheekey, J., Van de Voorde, G.: Rank-metric codes, linear sets, and their duality. Des. Codes Cryptogr. 88, 655–675 (2020)

    Article  MathSciNet  Google Scholar 

  8. Lidl, R., Niederreiter, H.: Finite Fields. Addison-Wesley (1983)

    Google Scholar 

  9. Zini, G., Zullo, F.: On the intersection problem for linear sets in the projective line. arXiv:2004.09441

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Authors and Affiliations

  1. UCD School of Mathematics and Statistics, University College Dublin, Dublin, Ireland

    Gary McGuire & John Sheekey

Authors
  1. Gary McGuire
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  2. John Sheekey
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Corresponding author

Correspondence to John Sheekey .

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Editors and Affiliations

  1. Sorbonne Paris, Paris, France

    Jean Claude Bajard

  2. Sabancı University, Istanbul, Turkey

    Alev Topuzoğlu

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McGuire, G., Sheekey, J. (2021). Linearized Polynomials and Their Adjoints, and Some Connections to Linear Sets and Semifields. In: Bajard, J.C., Topuzoğlu, A. (eds) Arithmetic of Finite Fields. WAIFI 2020. Lecture Notes in Computer Science(), vol 12542. Springer, Cham. https://doi.org/10.1007/978-3-030-68869-1_2

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  • DOI: https://doi.org/10.1007/978-3-030-68869-1_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-68868-4

  • Online ISBN: 978-3-030-68869-1

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