In this paper, we propose a mechanism on how to construct long MDS self-dual codes from short ones. These codes are special types of generalized Reed-Solomon (GRS) codes or extended generalized Reed-Solomon codes. The main tool is utilizing additive structure or multiplicative structure on finite fields. By applying this method, more MDS self-dual codes can be constructed.

中文翻译：

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从短代码构造长MDS自对码

在本文中，我们提出了一种从短码构造长MDS自对码的机制。这些代码是特殊类型的广义Reed-Solomon（GRS）码或扩展的广义Reed-Solomon码。主要工具是在有限域上利用加法结构或乘法结构。通过应用此方法，可以构造更多的MDS自对偶代码。