New Nonexistence Results on Circulant Weighing Matrices
A weighing matrix W = (wi,j) is a square matrix of order n and entries wi,j in {0,± 1} such that WWT = kIn. In his thesis, Strassler gave a table of existence results for circulant weighing matrices with n ≤ 200 and k ≤ 100. In the latest version of Strassler’s table given by Tan, there are 34 open cases remaining. In this paper, we give nonexistence proofs for 12 of these cases, report on preliminary searches outside Strassler’s table, and characterize the known proper circulant weighing matrices.
- Year: 2021
- Category: Secure & Resilient Systems
- Category: Radar Systems
- Tag: Design Of Communication Systems, Original Message, Threat Model, Bit Error, Batch Normalization Layer, Deep Learning Architectures, Family Of Codes
- Author: K. T. Arasu, Daniel M. Gordon, Yiran Zhang
- Released: Cryptography and Communications
Featured Riverside Research Author(s)
K. T. Arasu
K. T. Arasu (Member, IEEE) is a senior research scientist at Riverside Research in the Engineering and Support Solutions Group. He received the B.S. and M.S. degrees in mathematics from Panjab University, India, and the Ph.D. degree from The Ohio State University. Prior to joining Riverside Research, he was a professor with the Department of Mathematics and Statistics, Wright State University, for 35 years. He investigates novel techniques on error correcting codes, cryptography, data security and privacy, as well as topics at the intersection of machine learning, security, and information theory. He has published over 110 research papers. During his time as a professor at Wright State University, he was presented the Teaching Excellence Award from the College of Science and Mathematics, the Presidential Research Excellence Award, and the Trustees' Award for Faculty Excellence. He serves on the editorial board of several technical international journal publications.
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