Abstract
It was proved by J. Schatz that the covering radius of the second order Reed–Muller code RM(2,6) is 18 (Schatz (1981)). However, the covering radius of RM(2,7) has been an open problem for many years. In this paper, we prove that the covering radius of RM(2,7) is 40, which is the same as the covering radius of RM(2,7) in RM(3,7). As a corollary, we also find new upper bounds for the covering radius of RM(2,n), n=8,9,10.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
