报告题目 (Title)：达到Griesmer界的最优二元自正交码的研究（Binary self-orthogonal codes which meet the Griesmer bound or have optimal minimum distances）

报告人 (Speaker)： 施敏加 教授（安徽大学）

报告时间 (Time)：2023年4月14日(周五) 10：30

报告地点 (Place)：校本部F309

邀请人(Inviter)：张红莲、丁洋

主办部门：理学院数学系

报告摘要：Let dso(n, k) denote the largest minimum distance among all binary self-orthogonal [n, k] codes. The determination of dso(n, k) has been a fundamental and difficult problem in coding theory because there are too many binary self-orthogonal codes as the dimension k increases. First, we develop a general method to determine the exact value of dso(n, k) for k= 5, 6 and show that the two conjectures made by Kim and Choi in (IEEE Trans. Inf. Theory 2022, 68(11): 7159-7164.) are true. Further, we characterize the existence of binary self-orthogonal codes meeting the Griesmer bound by employing Solomon-Stiffler codes and some related residual codes. Using such a characterization, we determine the exact value of dso(n,7) except for five special cases. In addition, we develop a general method to prove the nonexistence of some binary self-orthogonal codes by considering the residual code of a binary self-orthogonal code.