AI 中文总结
本文研究GRS码的自同构结构，引入扭曲共轭作用，利用Shintani定理分类对合的γ_{p^j}-相似类，得到交替码具备射影半线性自同构诱导的中心对称结构的充要条件，实现了诱导中心对称交替码的统一分类。
AI 中文摘要
本文通过研究广义里德-所罗门（GRS）码继承的自同构结构，对诱导中心对称交替码进行分类。我们引入与射影半线性变换自然关联的扭曲共轭作用，建立其与射影半线性群中普通共轭的对应关系。该对应关系使Shintani定理可用于分类对合的γ_{p^j}-相似类，由此得到交替码具备由射影半线性自同构诱导的中心对称结构的充要条件，所得分类在基于自同构的统一框架下整合了不同族的诱导中心对称交替码。
英文摘要
This paper presents a classification of induced centrosymmetric alternant codes through the study of the automorphism structures inherited from Generalized Reed--Solomon (GRS) codes. We introduce the twisted conjugation action naturally associated with projective semilinear transformations and establish its correspondence with ordinary conjugacy in the projective semilinear group. This correspondence enables the application of Shintani's theorem to classify the $γ_{p^j}$-similarity classes of involutions. As a consequence, we obtain necessary and sufficient conditions for an alternant code to admit a centrosymmetric structure induced by a projective semilinear automorphism. The resulting classification unifies the different families of induced centrosymmetric alternant codes within a common automorphism-based framework.
Comments Keywords: Alternant codes, Generalized Reed--Solomon codes, automorphism groups, twisted conjugacy, projective semilinear group.
