Diagonally cyclic equitable rectangles

Anthony B. Evans, David Fear, Rebecca J. Stones

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

An equitable (r,c;v)-rectangle is an r×c matrix L=(lij) with symbols from (Formula presented.) in which each symbol appears in every row either (Formula presented.) or (Formula presented.) times and in every column either (Formula presented.) or (Formula presented.) times. We call L diagonally cyclic if l(i+1) (j+1)=lij+1, where the rows are indexed by (Formula presented.) and columns indexed by (Formula presented.). We give a constructive proof of necessary and sufficient conditions for the existence of a diagonally cyclic equitable (r,c;v)-rectangle.

Original languageEnglish
Pages (from-to)551-569
Number of pages19
JournalDesigns Codes and Cryptography
Volume76
Issue number3
DOIs
Publication statusPublished - 6 Sep 2015

Keywords

  • Equitable rectangle
  • Latin rectangle
  • Latin square
  • Orthogonal array

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