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On the Existence of de Bruijn Tori with Two by Two Windows

✍ Scribed by Glenn H. Hurlbert; Chris J. Mitchell; Kenneth G. Paterson

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
361 KB
Volume
76
Category
Article
ISSN
0097-3165

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✦ Synopsis

Necessary and sufficient conditions for the existence of de Bruijn Tori (or Perfect Maps) with two by two windows over any alphabet are given. This is the first twodimensional window size for which the existence question has been completely answered for every alphabet. The techniques used to construct these arrays utilise existing results on Perfect Factors and Perfect Multi-Factors in one and two dimensions and involve new results on Perfect Factors with `puncturing capabilities'. Finally, the existence question for two-dimensional Perfect Factors is considered and is settled for two by two windows and alphabets of prime-power size. 1996 Academic Press, Inc.

1. Introduction

A two-dimensional C-ary de Bruijn torus (or perfect map) is a twodimensional periodic array with symbols drawn from an alphabet of size C having the property that every C-ary array of some fixed size occurs exactly article no. 0102

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