报告题目 (Title)：线性插入删除码的的若干界和最优码的构造（Strict Half-Singleton Bound, Strict Direct Upper Bound for Linear Insertion-Deletion Codes and Optimal Codes）

报告人 (Speaker)： 郑大彬 教授（湖北大学）

报告时间 (Time)：2023年4月14日(周五) 09：30

报告地点 (Place)：校本部F309

邀请人(Inviter)：张红莲 教授

主办部门：理学院数学系

报告摘要：Let C be an [n, k] linear code over the finite field F_q. Let d_I(C) denote its insertion-deletion (insdel for short) distance, which characterizes the insdel error-correcting capability of C. In this paper we propose a strict half-Singleton upper bound d_I(\C) ≤2(n-2k+1)if C does not contain the codeword with all 1s, which generalizes the half-Singleton bound on the insdel distances of linear codes due to Cheng-Guruswami-Haeupler-Li, and a stronger direct upper bound d_I(C)≤2(d_H(C)-t) under a weak condition, where t≥1 is a positive integer determined by the generator matrix and d_H(C) denotes the Hamming distance of C. A sufficient condition for a linear code attaining the strict half-Singleton bound is given. We prove that the code length of an optimal binary linear insdel code w.r.t. the (strict) half- Singleton bound is about twice its dimension and conjecture that optimal binary linear insdel codes have exact parameters [2k, k, 4] or [2k+1, k, 4] w.r.t. the half- or strict half-Singleton bound, respectively.