题目：Binary self-orthogonal codes which meet the Griesmer bound or have optimal minimum distances

主 讲 人：施敏加 教授

时  间：2023年12月19日（周二） 9：00

地  点：腾讯会议（368-259-617）

主办单位：理学院

主讲人简介：

  施敏加，博士，二级教授，博士生导师，数学科学学院副院长。2020-2023连续四年入选全球前2%顶尖科学家“年度影响力”榜单，是SCI期刊JAMC的副主编。先后荣获安徽省自然科学一等奖和二等奖各一项，入选第二届“安徽省青年数学奖”，安徽省杰青、安徽省学术与技术带头人、高校学科(专业)拔尖人才计划。主持国家自然科学基金4项，安徽省杰青等省部级重点项目多项。在 Elsevier和World Scientific出版社主编出版英文学术专著 2 部，以第一作者/通信作者在IEEE Trans. Inform. Theory，JCTA等权威期刊上发表SCI论文130余篇，研究成果入选《世界简明编码理论百科全书》和ESI高被引论文。在科学出版社出版《近世代数》教材1部，是《近世代数》国家一流课程的负责人，获教育部宝钢优秀教师奖，安徽省教学名师、省级研究生导师师德标兵称号等。曾应邀访问新加坡，法国，俄罗斯、韩国等国家。

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.