Recent results on sequences with low autocorrelation

Prior to 1997, the most recent construction of binary sequences of period 2ⁿ-1 with ideal autocorrelation function came from the 1962 construction by Gordon, Mills and Welch. It is surprising therefore that the past three years have witnessed two parallel developments which have given rise to new families of sequences having ideal autocorrelation. The first development was the discovery by Maschietti (see Designs, Codes and Cryptography, vol.14, p.89-98, 1998) that certain well-studied combinatorial objects known as monomial hyperovals give rise to ideal sequences. The second relates to certain remarkable conjectures of No, Golomb, Gong, Lee, Gaal (see IEEE Trans. Inform. Theory, vol.44, p.814-17, 1998) and of No, Chung and Yun (see IEEE Trans. Inform. Theory, vol.44, p.1278-82, 1998). These conjectures were subsequently unified and enlarged by Dobbertin (see Proc. of the NATO ASI Workshop, Bad Windsheim, 1998). Also, Dobbertin and Dillon have succeeded in proving most of these conjectures, thereby identifying new families of previously unknown ideal sequences. This article provides an overview of these developments