A new optimal quaternary sequence family of length \(2(2^{n}-1)\) obtained from the orthogonal transformation of families \({\mathcal{B}}\) and \({\mathcal{C}}\). (English) Zbl 1183.94008
S. Boztas, R. Hammons and P. V. Kumar [IEEE Trans. Inform. Theory 38, 1101–1113 (1992; Zbl 0749.94011)], and P. Udaya and 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 [X. H. Tang and 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.
Reviewer: Wilfried Meidl (Istanbul)
MSC:
| 94A05 | Communication theory |
| 94A55 | Shift register sequences and sequences over finite alphabets in information and communication theory |
Keywords:
quaternary sequences; correlation; optimal sequences; Galois ring; orthogonal transformationReferences:
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