Twisted Hermitian Codes
Twisted Hermitian Codes
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DOI：
10.3390/math9010040
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发表时间：
2020-12
期刊：
影响因子：
2.4
通讯作者：
Austin Allen;Keller Blackwell;Olivia Fiol;Rutuja Kshirsagar;Bethany Matsick;Gretchen L. Matthews;Zoe Nelson
中科院分区：
文献类型：
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作者：
Austin Allen;Keller Blackwell;Olivia Fiol;Rutuja Kshirsagar;Bethany Matsick;Gretchen L. Matthews;Zoe Nelson
我们定义了一个称为扭曲的遗产代码的代码家族，该代码基于Hermitian代码，并受到Beelen，Puchinger和Nielsen所描述的扭曲的Reed的启发。我们确定了扭曲的Hermitian代码的亚家族，该代码可实现与随机线性代码接近的Schur Square尺寸。
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.