Source-pinned research

Research proof index

Search theorem names, mathematical ideas, modules, topics, projects, and role-labelled researchers. Open a result for its complete indexed Lean declaration and source record.

This index contains 6 research declarations. Search 10,000 more complete Mathlib declarations.

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Project-declaredLean 4.31.0

Reed Solomon multilinear Correlated Agreement Nat

reedSolomon_multilinearCorrelatedAgreement_Nat

Plain-language statement

Corollary 3.7: RS Codes have Tensor-Style Proximity Gaps (Unique Decoding) Example 4.1 shows that ε=n is tight for RS codes (Ben+23 Thm 4.1 is sharp).

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Dim eq card of lt

ReedSolomon.dim_eq_card_of_lt

Plain-language statement

The dimension of an RS-code equals the cardinality of the evaluation points if the original degree exceeds the cardinality.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Dim eq deg of le

ReedSolomon.dim_eq_deg_of_le

Plain-language statement

Dimension formula for RS code with arbitrary finite index type ι.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Gen Mat Is Vandermonde

ReedSolomon.genMatIsVandermonde

Plain-language statement

The Vandermonde matrix is the generator matrix for an RS code of length ι and dimension deg.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Relative Unique Decoding Radius RS eq

ReedSolomon.relativeUniqueDecodingRadius_RS_eq

Plain-language statement

Relative unique decoding radius for RS code with arbitrary finite index type ι.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

To Polynomial mem lt deg

ReedSolomon.toPolynomial_mem_lt_deg

Plain-language statement

The polynomials corresponding to Reed-Solomon codewords are of degree smaller than deg.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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