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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The above listed authors are current or former employees of Riverside Research. Authors affiliated with other institutions are listed on the full paper. It is the responsibility of the author to list material disclosures in each paper, where applicable – they are not listed here. This academic papers directory is published in accordance with federal guidance to make public and available academic research funded by the federal government.