In [4] Camps-Moreno et al. treated (relative) generalized Hamming weights of codes from extended norm-trace curves and they gave examples of resulting good asymmetric quantum error-correcting codes employing information on the relative distances. In the present paper we study ramp secret sharing schemes which are objects that require an analysis of higher relative weights and we show that not only do schemes defined from one-point algebraic geometric codes from extended norm-trace curves have good parameters, they also posses a second layer of security along the lines of [11]. It is left undecided in [4, page 2889] if the ``footprint-like approach'' as employed by Camps-Moreno herein is strictly better for codes related to extended norm-trace codes than the general approach for treating one-point algebraic geometric codes and their likes as presented in [12]. We demonstrate that the method used in [4] to estimate (relative) generalized Hamming weights of codes from extended norm-trace curves can be viewed as a clever application of the enhanced Goppa bound in [12] rather than a competing approach.

翻译：在文献[4]中，Camps-Moreno等人处理了扩展范数迹曲线所生成码的（相对）广义汉明重量，并利用相对距离信息给出了由此构造的良好非对称量子纠错码的实例。本文研究斜坡秘密共享方案——这类方案需要对更高阶相对重量进行分析，并证明：不仅基于扩展范数迹曲线单点代数几何码定义的方案具有优良参数，它们还具备如文献[11]所述的第二层安全性。文献[4]第2889页遗留了一个未决问题：Camps-Moreno等人采用的“类足迹方法”对于扩展范数迹曲线相关码的处理，是否严格优于文献[12]提出的针对单点代数几何码及其类似码的通用方法。我们证明，文献[4]中用于估计扩展范数迹曲线码（相对）广义汉明重量的方法，可视为对文献[12]中增强型Goppa界的巧妙应用，而非一种竞争性方法。