Abstract In Goppa (1970), V. D. Goppa presents a new family of linear codes over finite fields. This family, now known as Goppa codes, has been studied for nearly 50 years, including efficient decoding algorithms (Patterson, 1975) and its applications in cryptography (McEliece, 1978). Moreover, in Andrade et al. (2005), de Andrade and Palazzo present a generalization of Goppa codes to finite rings. Motivated by cryptographic applications, in this article we focus on Goppa codes over Z ∕ 4 Z and study some of their properties.

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关于四元 Goppa 码

摘要 在 Goppa (1970) 中，VD Goppa 提出了一个新的有限域线性码族。这个家族，现在被称为 Goppa 码，已经研究了近 50 年，包括有效的解码算法（Patterson，1975）及其在密码学中的应用（McEliece，1978）。此外，在安德拉德等人。(2005)，de Andrade 和 Palazzo 提出了 Goppa 码到有限环的推广。受密码学应用的启发，在本文中，我们重点讨论 Z ∕ 4 Z 上的 Goppa 码并研究它们的一些性质。