Information Technology Reference
In-Depth Information
5Conluon
The randomness properties of sequences generated by a function via the additive
order are studied in this paper. Some simple conditions are derived under which
such sequences have the maximum period. The autocorrelation of such sequences
is also studied, and one conjecture is presented. A nice approach for proving this
conjecture is desirable.
Acknowledgments
The work is supported by NSERC SPG Grant. The authors wish to thank the
anonymous reviewers for their helpful and valuable comments and suggestions.
Especially, the authors wish to thank Arne Winterhof for his comments which
made the proof of Theorem 1 extremely shorten and established the bound given
by Theorem 2.
References
1. Chen, Z.: Finite binary sequences constructed by explicit inversive methods. Finite
Fields Appl. (to appear)
2. Davis, J.A., Jedwab, J.: Peak-to-mean power control in OFDM, Golay comple-
mentary sequences and Reed-Muller codes. IEEE Trans. Inform. Theory 45(7),
2397-2417 (1999)
3. Golomb, S.W., Gong, G.: Signal Design for Good Correlation-For Wireless Com-
munication, Cryptography and Radar. Cambridge Univ. Press, Cambridge (2005)
(Section 6.6)
4. Lidl, R., Niederreiter, H.: Finite Fields. Addison-Wesley, Reading (1983) (now dis-
tributed by Cambridge Univ. Press)
5. Lipmaa, H., Rogaway, P., Wagner, D.: Comments to NIST concerning AES modes
of operations: CTR-mode encryption,
6. Mauduit, C., Niederreiter, H., Sarkozy, A.: On pseudorandom (0
,
1) and binary
sequences. Publ. Math. Debrecen. 71(3-4), 305-324 (2007)
7. Meidl, W., Winterhof, A.: On the autocorrelation of cyclotomic generator. In:
Mullen, G.L., Poli, A., Stichtenoth, H. (eds.) Fq7 2003. LNCS, vol. 2948, pp. 1-11.
Springer, Heidelberg (2003)
8. Moreno, C.J., Moreno, O.: Exponential sums and Goppa codes: I. Proc. Amer.
Math. Soc. 111, 523-531 (1991)
9. Niederreiter, H., Winterhof, A.: Incomplete exponential sums over finite fields
and their applications to new inversive pseudorandom number generators. Acta
Arith. 93, 387-399 (2000)
10. Paterson, K.G.: Generalized Reed-Muller codes and power control in OFDM mod-
ulation. IEEE Trans. Inform. Theory 46(1), 104-120 (2000)
