The Existence and Nonexistence of Optimal Binary Self-Orthogonal Codes

Abstract

First, we characterize the existence of binary self-orthogonal codes meeting the Griesmer bound by employing the Solomon-Stiffler codes. As a result, we reduce a problem with an infinite number of cases to a finite number of cases. Second, we develop some general methods involving residual codes, anticodes, and the MacWilliams identities to prove the nonexistence of some binary self-orthogonal codes. Finally, we focus on the minimum distances of optimal binary self-orthogonal codes with dimensions seven and eight.

Biography

Minjia Shi (Member, IEEE) received the Ph.D. degree from the Institute of Computer Network Systems, Hefei University of Technology, China, in 2010. From August 2012 to August 2013, he was a Visiting Researcher with the School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore. From July 2016 to August 2016, he was a Visiting Researcher with Telecom Paris Tech, Paris, France. Later, he visited the Sobolev Institute of Mathematics in 2020. He has been a Professor with the School of Mathematical Sciences, Anhui University, since 2017. He is the author of over 150 journal articles and three books. His research interests include algebraic coding theory, and cryptography. He is on the editorial board of IEEE TRANSACTIONS ON INFORMATION THEORY and Journal of Applied Mathematics and Computing.