Twisted Hermitian Codes

Austin Allen, Keller Blackwell, Olivia Fiol, Rutuja Kshirsagar, Bethany Matsick, Gretchen L. Matthews and Zoe Nelson
Additional contact information
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

Mathematics, 2020, vol. 9, issue 1, 1-14

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.

Keywords: algebraic geometry code; code-based cryptography; Hermitian code; Hermitian curve; McEliece cryptosystem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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