论文标题
两类线性代码的子字段代码
Two classes of subfield codes of linear codes
论文作者
论文摘要
最近，研究了带有良好参数的GF $（Q）上线性代码的子框代码，并获得了许多最佳子场代码。在本文中，我们主要的动机是纳入丁格和亨的子场的结果（有限领域的应用程序56、308-331（2019）），并纳入了Xiang和Yin和Yin的两个子场代码的结果（Cryptogr。我们获得这些子场代码的参数和权重分布。同时，还研究了其双重代码的参数。当$ m = 1 $时，这些子字段代码的双代码几乎是MDS代码，当$ m> 1 $和$ p $奇数时，相对于球形绑定的绑定，这些双重代码是最佳的尺寸。
Recently, subfiled codes of linear code over GF$ (q) $ with good parameters were studied, and many optimal subfield codes were obtained. In this paper, Our mainly motivation is to generlize the results of the subfield codes of hyperoval in Ding and Heng (Finite Fields Their Appl. 56, 308-331 (2019)), and generlize the results of two families of subfield codes in Xiang and Yin (Cryptogr. Commun. 13(1), 117-127 (2021)) to $ p $-ary where $ p $ is odd. We get the parameters and weight distribution of these subfield codes. At the same time, the parameters of their dual codes are also studied. When $ m=1 $, The dual codes of these subfield codes are almost MDS code, when $ m>1 $ and $ p $ odd, these dual codes are dimension-optimal with respect to the sphere-backing bound.
