Hermitian codes as generalized Reed-Solomon codes

1992 ◽  
Vol 2 (1) ◽  
pp. 5-17 ◽  
Author(s):  
Tomik Yaghoobian ◽  
Ian F. Blake
Keyword(s):  
Hermitian Codes ◽  
Reed Solomon Codes

scholarly journals Twisted Hermitian Codes

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 40
Author(s):  
Austin Allen ◽  
Keller Blackwell ◽  
Olivia Fiol ◽  
Rutuja Kshirsagar ◽  
Bethany Matsick ◽  
...  
Keyword(s):  
Linear Code ◽  
High Dimensional ◽  
Hermitian Codes ◽  
Reed Solomon Codes ◽  
New Codes

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.

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