Binary sequences with Merit Factor > 6.3
A method is described for the construction of binary sequences of very long length and with asymptotic Merit Factor > 6.3. The result is backed up by strong experimental evidence although no formal proof for the asymptote is known. The sequences were found by Kristiansen [1] using a small deterministic search, which we describe. Borwein, Choi, and Jedwab [2] have independently identified a Merit Factor asymptote of 6.3421.... After we became aware of their work we realized that the sequences we construct are more simply described as periodic extensions of periodically rotated Legendre sequences.
merit factor legendre sequence aperiodic autocorrelation l4 norm quadratic residue sequence