DocumentCode :
1205568
Title :
Perfect maps
Author :
Paterson, Kenneth G.
Author_Institution :
Dept. of Math., London Univ., UK
Volume :
40
Issue :
3
fYear :
1994
fDate :
5/1/1994 12:00:00 AM
Firstpage :
743
Lastpage :
753
Abstract :
Given positive integers r, s, u, and υ, an (r, s; u, υ) perfect map (PM) is defined to be a periodic r×s binary array in which every u×υ binary array appears exactly once as a periodic subarray. Perfect maps are the natural extension of the de Bruijn sequences to two dimensions. In the paper the existence question for perfect maps is settled by giving constructions for perfect maps for all parameter sets subject to certain simple necessary conditions. Extensive use is made of previously known constructions by finding new conditions which guarantee their repeated application. These conditions are expressed as bounds on the linear complexities of the periodic sequences formed from the rows and columns of perfect maps
Keywords :
binary sequences; computational complexity; bounds; columns; de Bruijn sequences; existence question; linear complexities; perfect map; periodic r×s binary array; periodic sequences; periodic subarray; rows; u×υ binary array;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/18.335886
Filename :
335886
Link To Document :
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