Barker sequences

formal-conjectures · arxiv · ams-5 · ams-11 · ams-94

A Barker sequence is a finite sequence of $\pm 1$ values whose nontrivial aperiodic
autocorrelations all have magnitude at most one. The Barker conjecture says that no such sequence
has length greater than $13$.

Every Barker sequence has length at most $13$.

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://arxiv.org/abs/2104.00502
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://en.wikipedia.org/wiki/Barker_code
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://oeis.org/A091704
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Arxiv/2104.00502/BarkerSequence.lean
Local target: Corpus.Arxiv210400502BarkerSequence.barker_conjecture
Source SHA-256: d42729cd1601f68a6b69c5316ef3843fcbd0abead3bfecd56ed7399b4ebfde6a
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record