Constructions for perfect maps and pseudorandom arrays

Authors:
T. Etzion
Affiliations:
Dept. of Electr. Eng.-Syst., Univ. of Southern California, Los Angeles, CA
Venue:
IEEE Transactions on Information Theory - Part 1
Year:
2006

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Abstract

A construction of perfect maps, i.e. periodic r×v binary arrays in which each n×m binary matrix appears exactly once, is given. A similar construction leads to arrays in which only the zero n×m matrix does not appear and to a construction in which only a few n×m binary matrices do not appear. A generalization to the nonbinary case is given. The constructions involve an interesting problem in shift-register theory. The solution is given for almost all the case of this problem