主讲人：汪馨 苏州大学副研究员
时间：2026年10月17日14：00
地点：徐汇校区三号楼301室
举办单位：数理学院
主讲人介绍：汪馨，现为苏州大学数学科学学院副研究员，研究方向为组合数学和编码理论，目前已在《IEEE Transactions on Information Theory》、《Finite fields and Their Applications》、《Designs, Codes and Cryptography》等高水平期刊上发表学术论文20余篇。
内容介绍：We study single error detection and correction for analog codes over the real numbers. The key performance measures are the parameters $\Gamma_1(\cC)$ and $\Gamma_2(\cC)$, which quantify, respectively, the minimum separation required between large outlying errors that must be detected or located and the magnitude of tolerable perturbations. We first establish a general lower bound on the single error detection parameter $\Gamma_1(\cC)$ for every real linear code in terms of its length and codimension. We then derive a lower bound on the single error correction parameter $\Gamma_2(\cC)$ for real linear codes of codimension two. These two bounds settle all four open problems posed by Roth concerning the optimality of single error detecting and single error correcting analog codes. The first bound is proved by a double induction argument, whereas the second follows from a geometric characterization based on zonotopes together with a cyclic sine product inequality.
