A class of balanced binary sequences with two-valued non-zero autocorrelation sum and good crosscorrelation sum

In this paper, we study a class of binary sequences with two-valued non-zero periodic autocorrelation sum and good periodic crosscorrelation sum as well as balanced properties. We make use of the sequences obtained in (No, J. et al., IEEE Trans. Inform. Theory 44(3), 1278-1282 2001) and adopt the extraction method similar to (Lüke, H. IEEE Trans. Inform. Theory 43(1) 1997). The new sequences are proven to be balanced or almost balanced. Based on these correlation and balanced properties, an important application is to construct Hadamard matrices of order \(p+1\) $p+1$ for \(p\equiv 3~(\) $p\equiv 3($ mod 4) and \(2p+2\) $2p+2$ for \(p\equiv 1~(\) $p\equiv 1($ mod 4). Some examples are shown to verify the theoretical results.