Existence of ideal matrices

Wai Chee SHIU*, Y. P. Tang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review


An m × n ideal matrix is a periodic m × n binary matrix which satisfies the following two conditions: (1) each column of this matrix contains precisely one 1 and (2) if it is visualized as a dot pattern (with each dot representing a 1), then the number of overlapping dots at all actual shifts are 1 or 0. Let s(n) denote the smallest integer m such that an m × n ideal matrix exists. In this paper, we reduce the upper bound of s(n) which was found by Fung, Siu and Ma. Also we list an upper bound of s(n) for 14 ≤ n ≤ 100.

Original languageEnglish
Pages (from-to)87-92
Number of pages6
JournalArs Combinatoria
Publication statusPublished - Dec 1997

Scopus Subject Areas

  • Mathematics(all)


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