Binary periodic sequences with 2-level autocorrelation values

Abstract

Binary sequences with low autocorrelation values have important applications in cryptography and communications. In this paper, we study binary periodic sequences with 2-level autocorrelation values. For n≡1(mod4), we prove some cases of Schmidt’s Conjecture for perfect binary sequences (Des. Codes Cryptogr. 78 (2016), 237-267). For n≡2(mod4), Jungnickel and Pott (1999) left the existence of four perfect binary sequences as an open question and we solve three of them. For n≡3(mod4), we present nonexistence of some binary sequences whose nontrivial autocorrelation values are all equal to 3. For n≡0(mod4), we give two binary sequences with d=4 for n=8,40, and also show that there do not exist such binary sequences for all other values of n.