Perfect hypercubes

Antal Iványi, János Madarász

Research output: Contribution to journalArticle


An (n, d, a, b)-perfect array is a d-dimensional b1×b2×...×bd sized n-ary periodic array containing all possible a1×a2×...×ad sized n-ary array exactly once as subarray. If a1=a2=...=ad and term double cube are used. If d≥4, then the double cube is called double hypercube. We prove the existence of (N, d, a, b)-perfect double cubes for arbitrary d≥1, a≥2 and n≥2, where N=kn with a suitable k≥1. Further we illustrate the main theorem constructing 4 and 5-dimensional hypercubes.

Original languageEnglish
Pages (from-to)475-480
Number of pages6
JournalElectronic Notes in Discrete Mathematics
Publication statusPublished - Dec 1 2011



  • De Bruijn arrays
  • Four- and five-dimensional perfect arrays
  • Perfect cubes

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this