On weight distributions of perfect colorings and completely regular codes

DOI10.1007/s10623-010-9479-4zbMath1235.94065arXiv0907.0001OpenAlexW3125362008WikidataQ21564023 ScholiaQ21564023MaRDI QIDQ648072

Denis S. Krotov

Publication date: 22 November 2011

Published in: Designs, Codes and Cryptography (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.0001

zbMATH Keywords

weight distributionweight enumeratorcompletely regular codeequitable partitionperfect coloringperfect structure

Mathematics Subject Classification ID

Other designs, configurations (05B30) Coloring of graphs and hypergraphs (05C15) Distance in graphs (05C12) Combinatorial codes (94B25)

Related Items (20)

On the non-existence of extended 1-perfect codes and MDS codes ⋮ Perfect 3-colorings of the Johnson graph \(J(6, 3)\) ⋮ Minimum supports of eigenfunctions of graphs: a survey ⋮ Minimum supports of eigenfunctions in bilinear forms graphs ⋮ Reconstruction of Eigenfunctions of q-ary n-Dimensional Hypercube ⋮ Completely regular codes in Johnson and Grassmann graphs with small covering radii ⋮ Perfect 2-colorings of the Johnson graph \(J(9, 4)\) ⋮ On the coset graph construction of distance-regular graphs ⋮ Local distributions and reconstruction of hypercube eigenfunctions ⋮ The minimum volume of subspace trades ⋮ To the theory of \(q\)-ary Steiner and other-type trades ⋮ Perfect 2‐colorings of Hamming graphs ⋮ On the binary codes with parameters of triply-shortened 1-perfect codes ⋮ Local duality theorem for \(q\)-ary 1-perfect codes ⋮ Local duality for equitable partitions of a Hamming space ⋮ Local distributions for eigenfunctions and perfect colorings of \(q\)-ary Hamming graph ⋮ On calculation of the interweight distribution of an equitable partition ⋮ Algebraic properties of perfect structures ⋮ On unbalanced Boolean functions with best correlation immunity ⋮ Harmonic Distributions for Equitable Partitions of a Hypercube

Cites Work

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• On new completely regular \(q\)-ary codes
• On weight distributions of shifts of Goethals-like codes
• Perfect colorings of the 12-cube that attain the bound on correlation immunity
• On the binary codes with parameters of doubly-shortened 1-perfect codes
• On perfect colorings of the halved 24-cube
• Perfect 2-Colorings of Johnson Graphs J(6,3) and J(7,3)
• A survey of perfect codes
• On perfect binary codes

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