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Additive skew G -codes over finite fields
Applicable Algebra in Engineering, Communication and Computing ( IF 0.7 ) Pub Date : 2021-05-15 , DOI: 10.1007/s00200-021-00515-6
S. T. Dougherty , Adrian Korban , Serap Şahinkaya , Deniz Ustun

We define additive skew G-codes over finite fields and discuss several dualities attached to these codes. We examine the properties of self-dual skew G-codes and in particular we show that the dual, under any duality, of an additive skew G-code is also an additive skew G-code. Additionally, we propose a matrix construction for additive skew G-codes and use it to construct several examples of extremal self-dual additive skew G-codes over the finite field \({\mathbb {F}}_4\). Such codes have a strong connection to quantum error correcting codes.



中文翻译:

有限域上的加性偏G码

我们定义了有限域上的加性偏G代码,并讨论了附加在这些代码上的几个对偶。我们检查了自我对偶偏斜G代码的性质,特别是,我们证明了在任何对偶性下,加性偏斜G代码也是对偶加性偏斜G代码。另外,我们提出了一个可加偏斜G码的矩阵构造,并使用它构造了有限域\({\ mathbb {F}} _ 4 \)上的极值自对偶可加偏G码的几个示例。这样的代码与量子纠错代码有很强的联系。

更新日期:2021-05-15
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