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等人研究了扩展范数迹曲线所构造码的（相对）广义汉明重量，并利用相对距离信息给出了由此产生的优质非对称量子纠错码实例。本文研究斜坡秘密共享方案——这类方案需要分析更高阶的相对重量，并证明基于扩展范数迹曲线单点代数几何码构建的方案不仅具有优良参数，还具备文献[11]所述的第二层安全特性。文献[4]第2889页未决的问题是：Camps-Moreno等人采用的“类足迹方法”对于扩展范数迹相关码的处理，是否严格优于文献[12]提出的处理单点代数几何码及其类似码的通用方法。我们证明，文献[4]中估计扩展范数迹曲线码（相对）广义汉明重量的方法，可视为文献[12]中增强型Goppa界的巧妙应用，而非竞争性方法。