Weight Enumeration and the Geometry of Linear Codes

DOI10.1002/sapm1976552119zbMath0331.05019OpenAlexW200851994MaRDI QIDQ4097305

Curtis Greene

Publication date: 1976

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/sapm1976552119

Mathematics Subject Classification ID

Combinatorial aspects of finite geometries (05B25) Combinatorial aspects of matroids and geometric lattices (05B35) Theory of error-correcting codes and error-detecting codes (94B99) Other special functions (33E99)

Related Items (41)

A generalization of the Whitney rank generating function ⋮ On paving matroids and a generalization of MDS codes ⋮ Latroids and their representation by codes over modules ⋮ Higher support matroids ⋮ On the evaluation at \((j,j^2)\) of the Tutte polynomial of a ternary matroid ⋮ Whitney Numbers of Combinatorial Geometries and Higher-Weight Dowling Lattices ⋮ Defining the \(q\)-analogue of a matroid ⋮ Harmonic Tutte polynomials of matroids ⋮ Weighted Tutte-Grothendieck polynomials of graphs ⋮ The geometry of geometries: matroid theory, old and new ⋮ A generalization of weight polynomials to matroids ⋮ Generalized weights of codes over rings and invariants of monomial ideals ⋮ Some matroids related to sum-rank metric codes ⋮ The Redei function of a relation ⋮ The Projectivization Matroid of a \(\boldsymbol{q}\) -Matroid ⋮ On matroids from self-orthogonal codes and their properties ⋮ Relations between Möbius and coboundary polynomials ⋮ Congruence conditions, parcels, and Tutte polynomials of graphs and matroids ⋮ Constructing rate \(1/p\) systematic binary quasi-cyclic codes based on the matroid theory ⋮ On the evaluation at \(( - \iota ,\iota )\) of the Tutte polynomial of a binary matroid ⋮ Dual complementary polynomials of graphs and combinatorial-geometric interpretation on the values of Tutte polynomial at positive integers ⋮ The free product of M-fuzzifying matroids1 ⋮ The Tutte polynomial of a morphism of matroids. III: Vectorial matroids ⋮ Some results on generalised Whitney functions ⋮ The Potts model and the Tutte polynomial ⋮ Orbit-counting polynomials for graphs and codes ⋮ Codes with the rank metric and matroids ⋮ Permutation codes ⋮ Covering radii are not matroid invariants ⋮ Thomas H. Brylawski (1944--2007) ⋮ Matroids, generalized networks, and electric network synthesis ⋮ Tutte polynomial, complete invariant, and theta series ⋮ The weight distribution of the coset leaders for some classes of codes with related parity-check matrices ⋮ Bicycle dimension and special points of the Tutte polynomial ⋮ The Tutte-Grothendieck ring ⋮ Combinatorial analysis. (Matrix problems, choice theory) ⋮ Wei-type duality theorems for rank metric codes ⋮ Intersection Theory for Embeddings of Matroids into Uniform Geometries ⋮ Demi-matroids from codes over finite Frobenius rings ⋮ Extensions of the critical theorem ⋮ Tutte Polynomials and Bicycle Dimension of Ternary Matroids

Cites Work

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• The Tutte polynomial
• On the Abstract Properties of Linear Dependence
• On the algebraic theory of graph colorings
• On dichromatic polynomials

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