Randomness and Representation of Span n Sequences

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.

• Type: Conference
• Year: 2007
• Where: SSC
• Authors: Guang Gong
• Keywords: Bruijn Sequences, Cryptography, Discrete Fourier Transform, Sequences, SSC 2007