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A new tower with good $p$-rank meeting Zink’s bound

Volume 177 / 2017

Nurdagül Anbar, Peter Beelen, Nhut Nguyen Acta Arithmetica 177 (2017), 347-374 MSC: Primary 14H05, 11G20; Secondary 14G50. DOI: 10.4064/aa8388-6-2016 Published online: 18 January 2017

Abstract

We investigate the asymptotic $p$-rank of a new tower of function fields defined over cubic finite fields. Its limit meets Zink’s bound, but the new feature of this tower is that its asymptotic $p$-rank for small cubic finite fields is much smaller than that of other cubic towers for which the asymptotic $p$-rank is known. This is of independent interest, but also makes this new tower more interesting for theoretical applications in cryptography.

Authors

  • Nurdagül AnbarDepartment of Applied Mathematics and Computer Science
    Technical University of Denmark
    2800 Kongens Lyngby, Denmark
    e-mail
  • Peter BeelenDepartment of Applied Mathematics and Computer Science
    Technical University of Denmark 2800 Kongens Lyngby, Denmark
    e-mail
  • Nhut NguyenDepartment of Applied Mathematics and Computer Science
    Technical University of Denmark
    2800 Kongens Lyngby, Denmark
    e-mail

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