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必赢242net2023年学术报告系列讲座(二十九)

发布于:2023-12-15 浏览:

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

:施敏加 教授

  20231219日(周二) 900

  :腾讯会议(368-259-617

主办单位:必赢242net

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 ElsevierWorld 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. TheoryJCTA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.

 

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