Golomb’s Randomness Postulates

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Related Concepts

Autocorrelation; Gap; Maximal-Length Linear Sequences; Pseudo-Noise Sequences (PN-Sequences); Run; Sequences

Definition

Golomb’s randomness postulates are three properties that one expects to find in random sequences.

Theory and Applications

No finite sequence constructed by a linear feedback shift register is a truly random sequence. Golomb [1] introduced the notion of a pseudo-random sequence for a periodic binary sequence that satisfies three randomness postulates. These postulates reflect the properties one would expect to find in a random sequence.

A run in a binary sequence is a set of consecutive 0s or 1s. A run of0s is denoted a gap and a run of 1s is denoted a block. A gap of length k is a set of k consecutive 0s flanked by 1s. A block of length k is a set of k consecutive 1s flanked by 0s. A run of length k is is a gap of length k or a block of length k. In this terminology, the three randomness postulates of a perio