A new optimal quaternary sequence family of length \(2(2^{n}-1)\) obtained from the orthogonal transformation of families \({\mathcal{B}}\) and \({\mathcal{C}}\) (Q1039267)

\textit{S. Boztas, R. Hammons} and \textit{P. V. Kumar} [IEEE Trans. Inform. Theory 38, 1101--1113 (1992; Zbl 0749.94011)], and \textit{P. Udaya} and \textit{M. U. Siddiqi} [Appl. Algebra Engrg. Comm. Comput. 9, 161--191 (1998; Zbl 0921.94009)] presented families, family \(\mathcal{B}\) respectively \(\mathcal{C}\), of quaternary \(2(2^n-1)\)-periodic sequences with the low maximal correlation \(2^{(n+1)/2}+2\) and family size \(2^{n-1}\). The authors propose a transformation on the sequence families \(\mathcal{B}\) and \(\mathcal{C}\) which doubles the size of the families and preserves the maximal correlation. The first family obtained in this way is the family \(\mathcal{D}\) introduced in [\textit{X. H. Tang} and \textit{P. Udaya}, IEEE Trans. Inform. Theory 53, 433--436 (2007)], the second family \(\mathcal{E}\) is new. For the new family \(\mathcal{E}\) the correlation distribution which is different to that of family \(\mathcal{D}\) is presented.