| import OAI.LinearAlgebra.CirculantHadamard.Model | |
| import Lean.Elab.Tactic.Omega | |
| namespace OAI | |
| namespace CirculantHadamard.Barker | |
| open scoped BigOperators | |
| def aperiodic {n : ℕ} (h : Fin n → ℤ) (k : ℕ) : ℤ := | |
| ∑ j : Fin (n - k), h ⟨j.val, by omega⟩ * h ⟨j.val + k, by omega⟩ | |
| def periodic {n : ℕ} [NeZero n] (h : Fin n → ℤ) (a : Fin n) : ℤ := | |
| ∑ j : Fin n, h j * h (j - a) | |
| def IsBarker {n : ℕ} (h : Fin n → ℤ) : Prop := | |
| (∀ j, IsSign (h j)) ∧ ∀ k : ℕ, 0 < k → k < n → |aperiodic h k| ≤ 1 | |
| end CirculantHadamard.Barker | |
| end OAI | |