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[4]中，Camps-Moreno等人处理了来自扩展范数迹曲线的码的（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好非对称量子纠错码的例子。本文研究斜坡秘密共享方案，这类对象需要分析更高阶的相对重量，我们证明，不仅从扩展范数迹曲线的一点点代数几何码定义的方案具有好的参数，它们还拥有沿[11]思路的第二层安全性。[4, 第2889页]未确定Camps-Moreno在此采用的“类足迹方法”是否严格优于[12]中处理一-点代数几何码及其类似码的一般方法。我们证明，[4]中用于估计来自扩展范数迹曲线码的（相对）广义汉明重量的方法，可视为[12]中增强Goppa界的巧妙应用，而非一种竞争性方法。