Twisted Hermitian Codes
| dc.contributor.author | Allen, Austin | en |
| dc.contributor.author | Blackwell, Keller | en |
| dc.contributor.author | Fiol, Olivia | en |
| dc.contributor.author | Kshirsagar, Rutuja | en |
| dc.contributor.author | Matsick, Bethany | en |
| dc.contributor.author | Matthews, Gretchen L. | en |
| dc.contributor.author | Nelson, Zoe | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2021-01-08T15:49:05Z | en |
| dc.date.available | 2021-01-08T15:49:05Z | en |
| dc.date.issued | 2020-12-26 | en |
| dc.date.updated | 2021-01-08T14:44:06Z | en |
| dc.description.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. | en |
| dc.description.version | Published version | en |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.citation | Allen, A.; Blackwell, K.; Fiol, O.; Kshirsagar, R.; Matsick, B.; Matthews, G.L.; Nelson, Z. Twisted Hermitian Codes. Mathematics 2020, 9, 40. | en |
| dc.identifier.doi | https://doi.org/10.3390/math9010040 | en |
| dc.identifier.uri | http://hdl.handle.net/10919/101798 | en |
| dc.language.iso | en | en |
| dc.publisher | MDPI | en |
| dc.rights | Creative Commons Attribution 4.0 International | en |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | en |
| dc.subject | algebraic geometry code | en |
| dc.subject | code-based cryptography | en |
| dc.subject | Hermitian code | en |
| dc.subject | Hermitian curve | en |
| dc.subject | McEliece cryptosystem | en |
| dc.title | Twisted Hermitian Codes | en |
| dc.title.serial | Mathematics | en |
| dc.type | Article - Refereed | en |
| dc.type.dcmitype | Text | en |