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J. Found. Comput. Sci."],"published-print":{"date-parts":[[2026,4]]},"abstract":"<jats:p>Hall\u2019s sextic residue sequences of prime period p with [Formula: see text] have some desirable features of pseudorandomness, such as high linear complexity, two-level periodic autocorrelation, nice aperiodic auto-correlation measure (correlation measure of order k) and in particular the 2-adic complexity for some special p (related to Hall\u2019s difference set). In this study, we prove a lower bound on the 2-adic complexity for all p, which implies that the 2-adic complexity of Hall\u2019s sequences is at least the expected value of the 2-adic complexity of all p-periodic binary sequences. 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