This paper presents a new family of linear codes, namely the expanded Gabidulin codes. Exploiting the existing fast decoder of Gabidulin codes, we propose an efficient algorithm to decode these new codes when the noise vector satisfies a certain condition. Furthermore, these new codes enjoy an excellent error-correcting capability because of the optimality of their parent Gabidulin codes. Based on different masking techniques, we give two encryption schemes by using expanded Gabidulin codes in the McEliece setting. According to our analysis, both of these two cryptosystems can resist the existing structural attacks. Our proposals have an obvious advantage in public-key representation without using the cyclic or quasi-cyclic structure compared to some other code-based cryptosystems.

翻译：本文展示了一套新的线性代码, 即扩大的加比杜林代码。 利用加比杜林代码的快速解码器, 我们提出一种有效的算法, 以便在噪音矢量满足特定条件时解码这些新代码。 此外, 这些新代码由于其父体加比杜林代码的最佳性而享有极佳的纠正错误能力。 基于不同的掩码技术, 我们通过在麦克利斯设置中使用扩大的加比杜林代码来提供两种加密方案。 根据我们的分析, 这两种加密系统都能够抵抗现有的结构攻击。 我们的建议在公共钥匙代表方面有着明显的优势, 而不使用循环或准循环结构, 与其他基于代码的加密系统相比。