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Twisted Hermitian Codes

Author

Listed:
  • Austin Allen

    (Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA)

  • Keller Blackwell

    (Department of Computer Science, Stanford University, Stanford, CA 94305, USA)

  • Olivia Fiol

    (Department of Mathematics and Statistics, Vassar College, Poughkeepsie, NY 12604, USA)

  • Rutuja Kshirsagar

    (Department of Mathematics, Virginia Polytechnic Institute & State University (Virginia Tech), Blacksburg, VA 24061, USA)

  • Bethany Matsick

    (Department of Mathematics, Liberty University, Lynchburg, VA 24515, USA)

  • Gretchen L. Matthews

    (Department of Mathematics, Virginia Polytechnic Institute & State University (Virginia Tech), Blacksburg, VA 24061, USA)

  • Zoe Nelson

    (Department of Mathematics, Oglethorpe University, Atlanta, GA 30319, USA)

Abstract

We define a family of codes called twisted Hermitian codes, which are based on Hermitian codes and inspired by the twisted Reed–Solomon codes described by Beelen, Puchinger, and Nielsen. We demonstrate that these new codes can have high-dimensional Schur squares, and we identify a subfamily of twisted Hermitian codes that achieves a Schur square dimension close to that of a random linear code. Twisted Hermitian codes allow one to work over smaller alphabets than those based on Reed–Solomon codes of similar lengths.

Suggested Citation

  • Austin Allen & Keller Blackwell & Olivia Fiol & Rutuja Kshirsagar & Bethany Matsick & Gretchen L. Matthews & Zoe Nelson, 2020. "Twisted Hermitian Codes," Mathematics, MDPI, vol. 9(1), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2020:i:1:p:40-:d:468815
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