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Merged
alexanderlhicks merged 3 commits into from
Jan 11, 2026
Merged

Resolving issue #217 #285

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e367bf4
added checkMatrix definition
DimitriosMitsios Jan 5, 2026
54a80fa
changes due to style guide
DimitriosMitsios Jan 9, 2026
4370c2e
Merge branch 'main' into main
DimitriosMitsios Jan 10, 2026
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10 changes: 5 additions & 5 deletions ArkLib/Data/CodingTheory/ReedSolomon.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -48,15 +48,15 @@ noncomputable def codewordToPoly
{deg : ℕ} {domain : ι ↪ F} (f : code domain deg) : F[X] :=
Lagrange.interpolate Finset.univ domain.toFun f

variable [Semiring F]

/-- The generator matrix of the Reed-Solomon code of degree `deg` and evaluation points `domain`. -/
def genMatrix (deg : ℕ) : Matrix (Fin deg) ι F :=
def genMatrix (deg : ℕ) [Semiring F] : Matrix (Fin deg) ι F :=
.of fun i j => domain j ^ (i : ℕ)

/-- The (parity)-check matrix of the Reed-Solomon code, assuming `ι` is finite. -/
def checkMatrix (deg : ℕ) [Fintype ι] : Matrix (Fin (Fintype.card ι - deg)) ι F :=
sorry
noncomputable def checkMatrix (deg : ℕ) [Fintype ι] [Field F] :
Matrix (Fin (Fintype.card ι - deg)) ι F :=
let P := Finset.univ.prod fun j => (X - C (domain j))
.of fun i j => domain j ^ (i : ℕ) * (P.derivative.eval (domain j))⁻¹

-- theorem code_by_genMatrix (deg : ℕ) :
-- code deg = codeByGenMatrix (genMatrix deg) := by
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