Generalized linkage construction for constant-dimension codes

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Abstract

A constant-dimension code (CDC) is a set of sub-spaces of constant dimension in a common vector space with upper bounded pairwise intersection. We improve and generalize two constructions for CDCs, the improved linkage construction and the parallel linkage construction, to the generalized linkage construction and the multiblock generalized linkage construction which in turn yield many improved lower bounds for the cardinalities of CDCs; a quantity not known in general.

Original languageEnglish
Article number9261394
Pages (from-to)705-715
Number of pages11
JournalIEEE Transactions on Information Theory
Volume67
Issue number2
Early online date2020
DOIs
Publication statusPublished - Feb 2021
MoE publication typeA1 Journal article-refereed

Keywords

  • combinatorics
  • constant-dimension codes
  • Couplings
  • Encoding
  • Extraterrestrial measurements
  • Finite projective spaces
  • lifted maximum rank-distance bound
  • Linear matrix inequalities
  • Manuals
  • Matrix decomposition
  • maximum rank-distance codes
  • rank distance
  • rank-metric codes
  • subspace codes
  • subspace-distance
  • Upper bound

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