Randomness and representation of span n sequences

Authors:
Guang Gong
Affiliations:
Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario, Canada
Venue:
SSC'07 Proceedings of the 2007 international conference on Sequences, subsequences, and consequences
Year:
2007

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Abstract

Any span n sequences can be regarded as filtering sequences. From this observation, new randomness criteria for span n sequences are proposed. It is proved that the feedback function of a span n sequence can be represented as a composition of its trace representation, or equivalently, its discrete Fourier transform, and a permutation from the state space of the sequence to the multiplicative group of the finite field GF(2n), and vice versa. Significant enhancements for randomness of span n sequences, so that de Bruijn sequences, are illustrated by some examples.