New Families of Ideal 2-Level Autocorrelation Ternary Sequences From Second Order DHT

Abstract

Abstract Following the work of Gong and Golomb on binary sequences, we used the technique of applying Second Order Decimation-Hadamard Transform (DHT) operater to obtain previously unknown ternary (ideal) two-level autocorrelation sequences. This process is referred to as realization. We obtained new multi-term ternary two-level autocorrelation sequences as realization of single 2-term ternary two-level autocorrelation sequence. We conjecture that for n = 2m + 1 odd, there exist m or m − 1 infinite inequivalent families of ternary two-level autocorrelation (AC) sequence which are given by four constructions. We have verified this for n = 5, 7, 9 and 11. Experimental results are provided.