Abstract
In this paper, we present some fundamental concepts and theoretical advances attributable to Solomon Golomb, together with the history and applications of this paper to communications, coding, and cryptography, along with some long-standing conjectures. Examples include the first engineering problem relating to feedback shift-register sequences that Sol Golomb was asked to solve in the mid-1950s. This paper covers $m$ -sequences and Golomb’s three randomness postulates, the cross-correlation of $m$ -sequences, the exp-Golomb code, the Golomb ruler, Costas arrays, Golomb invariants, polyominoes, the distribution of prime numbers, and irreducible polynomials.
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