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On sequences with zero autocorrelation

Journal Article


Abstract


  • Normal sequences of lengths n=18, 19 are constructed. It is proved through an exhaustive search that normal sequences do not exist for n=17, 21, 22, 23. Marc Gysin has shown that normal sequences do not exist for n=24. So the first unsettled case is n=27. Base sequences of lengths 2 n-1, 2 n-1, n, n are constructed for all decompositions of 6 n-2 into four squares for n=2, 4, 6, ..., 20 and some base sequences for n=22, 24 are also given. So T-sequences (T-matrices) of length 71 are constructed here for the first time. This gives new Hadamard matrices of orders 213, 781, 1349, 1491, 1633, 2059, 2627, 2769, 3479, 3763, 4331, 4899, 5467, 5609, 5893, 6177, 6461, 6603, 6887, 7739, 8023, 8591, 9159, 9443, 9727, 9869. © 1994 Kluwer Academic Publishers.

Publication Date


  • 1994

Citation


  • Koukouvinos, C., Kounias, S., Seberry, J., Yang, C. H., & Yang, J. (1994). On sequences with zero autocorrelation. Designs, Codes and Cryptography, 4(3), 327-340. doi:10.1007/BF01388649

Scopus Eid


  • 2-s2.0-0007152303

Web Of Science Accession Number


Start Page


  • 327

End Page


  • 340

Volume


  • 4

Issue


  • 3

Abstract


  • Normal sequences of lengths n=18, 19 are constructed. It is proved through an exhaustive search that normal sequences do not exist for n=17, 21, 22, 23. Marc Gysin has shown that normal sequences do not exist for n=24. So the first unsettled case is n=27. Base sequences of lengths 2 n-1, 2 n-1, n, n are constructed for all decompositions of 6 n-2 into four squares for n=2, 4, 6, ..., 20 and some base sequences for n=22, 24 are also given. So T-sequences (T-matrices) of length 71 are constructed here for the first time. This gives new Hadamard matrices of orders 213, 781, 1349, 1491, 1633, 2059, 2627, 2769, 3479, 3763, 4331, 4899, 5467, 5609, 5893, 6177, 6461, 6603, 6887, 7739, 8023, 8591, 9159, 9443, 9727, 9869. © 1994 Kluwer Academic Publishers.

Publication Date


  • 1994

Citation


  • Koukouvinos, C., Kounias, S., Seberry, J., Yang, C. H., & Yang, J. (1994). On sequences with zero autocorrelation. Designs, Codes and Cryptography, 4(3), 327-340. doi:10.1007/BF01388649

Scopus Eid


  • 2-s2.0-0007152303

Web Of Science Accession Number


Start Page


  • 327

End Page


  • 340

Volume


  • 4

Issue


  • 3