Abstract
A sequence u over a finite field F q is called an (f(x), m)-interleaved sequence [1] if f (x) is a common characteristic polynomial of all its m-decimated sequences. This paper demonstrates how the subjects such as the minimal polynomial, the linear span, the period and the correlation values of an (f(x),m)-interleaved sequence are related to its m-decimated sequences when f (x) is irreducible, and makes a correction to an error made in [1] in studying the same problem. Moreover, this paper shows how to choose the rn-decimated sequences to construct some sequences with the optimal auto and cross correlation values and maximal period among all the (f (x), m)-interleaved sequences when f (x) is primitive and m is less than the period of f (x).
The work is supported by the Chinese Natural Science Foundation.
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Shaoquan, J., Zongduo, D., Guang, G. (1999). Notes on q-ary Interleaved Sequences. In: Ding, C., Helleseth, T., Niederreiter, H. (eds) Sequences and their Applications. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0551-0_20
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DOI: https://doi.org/10.1007/978-1-4471-0551-0_20
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