Nonbinary Sequences with Superior Merit Factors

Abstract

Binary sequences with maximally large merit factors has been a topic for active search. Recently, it has been shown that superior merit factors can be obtained with ternary sequences (−1, 0, +1 as alphabet). However, only sequences with odd lengths were listed, with a belief that odd lengths permit larger merit factors. To test that belief and also to complement that work, ternary sequences with even lengths are listed here. The listing is based on the eugenic and SIKH algorithms developed recently. Using these algorithms it is shown that quinquenary sequences (−2, −1, 0, +1, +2 as alphabet) yield significantly larger merit factors. These results open a question whether one should stick to binary sequences for their engineering advantages.