Duality of codes supported on regular lattices, with an application to enumerative combinatorics

DOI10.1007/s10623-017-0436-3zbMath1411.94101arXiv1510.02383OpenAlexW2962880178MaRDI QIDQ1650813

Alberto Ravagnani

Publication date: 13 July 2018

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

Full work available at URL: https://arxiv.org/abs/1510.02383

zbMATH Keywords

weight functionMacWilliams identityweight distributionextremal codeenumerative combinatoricsdistance distributionadditive code (finite abelian group)poset latticesupport map

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Finite abelian groups (20K01) Combinatorial codes (94B25)

Related Items (8)

Covering Radius of Matrix Codes Endowed with the Rank Metric ⋮ Rank-Metric Codes, Semifields, and the Average Critical Problem ⋮ Generalized weights of codes over rings and invariants of monomial ideals ⋮ Rank-metric codes and \(q\)-polymatroids ⋮ Rank-metric codes, generalized binomial moments and their zeta functions ⋮ Partitions of matrix spaces with an application to \(q\)-rook polynomials ⋮ An Assmus--Mattson Theorem for Rank Metric Codes ⋮ Rook Theory of the Finite General Linear Group

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