Lower Bounds on Two-Dimensional Generalized Orthogonal Sequences

Fanxin ZENG  Zhenyu ZHANG  Lijia GE  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.4   pp.1140-1144
Publication Date: 2006/04/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.4.1140
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Information Theory
sequence,  two dimensional,  ZCZ,  generalized orthogonal,  complementary,  bound,  

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For various applications in image, communications and signal processing, two-dimensional (2-D) generalized orthogonal (GO) sequences, that is, 2-D sequences with zero correlation zone (ZCZ) and 2-D complementary orthogonal (CO) sequences with ZCZ, are widely investigated. New lower bounds for 2-D GO sequences, based on matrix theory on rank, are derived and presented, some examples that attain these lower bounds are given. As a direct application to our results, upper bound on family size of 2-D mutually complementary orthogonal (MCO) codes defined by Luke [9] is proposed.