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cdec422 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | 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
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