Abstract
For odd n, binary sequences of period 2n–1 with ideal two-level autocorrelation are investigated with respect to 3- or 5-valued crosscorrelation property between them. At most 5-valued crosscorrelation of m-sequences is first discussed, which is linked to crosscorrelation of some other binary two-level autocorrelation sequences. Then, several theorems and conjectures are established for describing 3- or 5-valued crosscorrelation of a pair of binary two-level autocorrelation sequences.
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This work was supported by NSERC Grant RGPIN 227700-00.
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References
Antweiler, M.: Cross-correlation of p-ary GMW sequences. IEEE Trans. Inform. Theory 40, 1253–1261 (1994)
Chang, A., Gaal, P., Golomb, S.W., Gong, G., Helleseth, T., Kumar, P.V.: On a conjectured ideal autocorrelation sequence and a related triple-error correcting cyclic code. IEEE Trans. Inform. Theory 46(2), 680–687 (2000)
Dillon, J.F., Dobbertin, H.: New cyclic difference sets with Singer parameters. Finite Fields and Their Applications 10, 342–389 (2004)
Dillon, J.F.: Multiplicative difference sets via additive characters. Designs, Codes and Cryptography 17, 225–235 (1999)
Games, R.A.: Crosscorrelation of m-sequences and GMW-sequences with the same primitive polynomial. Discrete Applied Mathematics 12, 139–146 (1985)
Gold, R.: Maximal recursive sequences with 3-valued recursive cross-correlation functions. IEEE Trans. Inform. Theory 14, 154–156 (1968)
Gong, G., Golomb, S.W.: The decimation-Hadamard transform of two-level autocorrelation sequences. IEEE Trans. Inform. Theory 48(4), 853–865 (2002)
Gordon, B., Mills, W.H., Welch, L.R.: Some new difference sets. Canadian Journal of Mathematics 14(4), 614–625 (1962)
Helleseth, T., Kumar, P.V.: Sequences with Low Correlation. In: Pless, V., Huffmann, C. (eds.) A chapter in Handbook of Coding Theory. Elsevier Science Publishers, Amsterdam (1998)
Hertel, D.: Cross-correlation properties of perfect binary sequences. In: Helleseth, T., Sarwate, D., Song, H.-Y., Yang, K. (eds.) SETA 2004. LNCS, vol. 3486, pp. 208–219. Springer, Heidelberg (2005)
Kasami, T.: Weight enumerators for several classes of subcodes of the 2nd-order Reed-Muller codes. Information and Control 18, 369–394 (1971)
Maschietti, A.: Difference sets and hyperovals. Designs, Codes and Cryptography 14, 89–98 (1998)
Niho, Y.: Multi-valued cross-correlation functions between two maximal linear recursive sequences. Ph.D. Dissertation. University of Southern California (1972)
No, J.S., Chung, H.C., Yun, M.S.: Binary pseudorandom sequences of period 2m − 1 with ideal autocorrelation generated by the polynomial z d + (z + 1)d. IEEE Trans. Inform. Theory 44(3), 1278–1282 (1998)
No, J.S., Golomb, S.W., Gong, G., Lee, H.K., Gaal, P.: Binary pseudorandom sequences of period 2m − 1 with ideal autocorrelation. IEEE Trans. Inform. Theory 44(2), 814–817 (1998)
Sidelnikov, V.M.: On mutual correlation of sequences. Soviet Math. Dokl 12, 197–201 (1971)
Welch, L.R.: Lower bounds on the maximum cross correlation of signals. IEEE Trans. Inform. Theory IT-20, 397–399 (1974)
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Yu, N.Y., Gong, G. (2006). Crosscorrelation Properties of Binary Sequences with Ideal Two-Level Autocorrelation. In: Gong, G., Helleseth, T., Song, HY., Yang, K. (eds) Sequences and Their Applications – SETA 2006. SETA 2006. Lecture Notes in Computer Science, vol 4086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11863854_9
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DOI: https://doi.org/10.1007/11863854_9
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