Reconstructing Sets of Latin Squares, Linear and Equivalent to Linear Codes

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Abstract

We consider the reconstruction problem concerning latin squares, sets of mutually orthogonal latin squares as well as linear and equivalent to linear codes in a vector space over a finite field. With regard to this problem we discuss related topics on intersection of combinatorial objects of the same class. An algorithm reconstructing latin squares and its sets is presented. By this way it is shown for q 3, 4, 5, 7 that the Bose complete set of mutually orthogonal latin squares of order q with 2q-1 or less blank entries in each square at the same places is reconstructed uniquely. We also point some recently obtained results on the maximum intersection of linear and equivalent to linear codes, and their applications as well.

Original languageEnglish
Title of host publication2019 16th International Symposium "Problems of Redundancy in Information and Control Systems", REDUNDANCY 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages47-51
Number of pages5
ISBN (Electronic)9781728119441
DOIs
Publication statusPublished - Oct 2019
Event16th International Symposium "Problems of Redundancy in Information and Control Systems", REDUNDANCY 2019 - Moscow, Russian Federation
Duration: 21 Oct 201925 Oct 2019

Publication series

Name2019 16th International Symposium "Problems of Redundancy in Information and Control Systems", REDUNDANCY 2019

Conference

Conference16th International Symposium "Problems of Redundancy in Information and Control Systems", REDUNDANCY 2019
Country/TerritoryRussian Federation
CityMoscow
Period21.10.201925.10.2019

Keywords

  • complete set of MOLS
  • equivalent codes
  • finite field
  • intersection
  • isometry
  • isotopy
  • latin square
  • linear code
  • MDS code
  • MOLS
  • pseudolinear code
  • reconstructing algorithm

OECD FOS+WOS

  • 1.02 COMPUTER AND INFORMATION SCIENCES

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