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 573 research declarations. Search 10,000 more complete Mathlib declarations.

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Project-declaredLean 4.31.0

Gs degree bound div lt

gs_degree_bound_div_lt

Plain-language statement

The GS degree bound with m=1 divided by (k-1) is less than F when |F| ≥ 5 and the RS code is non-degenerate (k+1 ≤ n ≤ F).

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Card constraint Indices

GuruswamiSudan.card_constraintIndices

Plain-language statement

The indices of constraints are m * (m + 1) / 2.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Card weigth Bound Indices eq sum

GuruswamiSudan.card_weigthBoundIndices_eq_sum

Plain-language statement

The number of variables is the sum over j of the number of valid i's.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Coeff linear Combination monomial

GuruswamiSudan.coeff_linearCombination_monomial

Plain-language statement

The coefficient of X^i Y^j in a linear combination of monomials is the coefficient of the combination.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Coeff vec to bivariate coeff

GuruswamiSudan.coeff_vec_to_bivariate_coeff

Plain-language statement

Coefficient extraction for coeffVecToBivariate: the (i, j)-coefficient of the bivariate polynomial equals c(i, j) when (i, j) is in the weighted-degree region.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.31.0

Degree eval le weighted Degree

GuruswamiSudan.degree_eval_le_weightedDegree

Plain-language statement

The degree of Q(X, P(X)) is bounded by the (1, k-1)-weighted degree of Q, provided deg(P) ≤ k - 1.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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