### Abstract

An equitable (r,c;v)-rectangle is an r×c matrix L=(l_{ij}) 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})=l_{ij}+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 language | English |
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Pages (from-to) | 551-569 |

Number of pages | 19 |

Journal | Designs Codes and Cryptography |

Volume | 76 |

Issue number | 3 |

DOIs | |

Publication status | Published - 6 Sep 2015 |

### Keywords

- Equitable rectangle
- Latin rectangle
- Latin square
- Orthogonal array

## Cite this

Evans, A. B., Fear, D., & Stones, R. J. (2015). Diagonally cyclic equitable rectangles.

*Designs Codes and Cryptography*,*76*(3), 551-569. https://doi.org/10.1007/s10623-014-9977-x