2015/10/29 by Qichun Wang, Wang, Qichun
Computer Science · Engineering · #Coding theory and cryptography #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1510.08535
openalex publication_date 2015/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1981, Schatz proved that the covering radius of the binary Reed-Muller code RM(2,6) is 18. For RM(2,7), we only know that its covering radius is between 40 and 44. In this paper, we prove that the covering radius of the binary Reed-Muller code RM(2,7) is at most 42. Moreover, we give a sufficient and necessary condition for Boolean functions of 7-variable to achieve the second-order nonlinearity 42.