Super-simple cyclic designs with small values

Super-simple cyclic designs are useful on constructing codes and designs such as superimposed codes, perfect hash families and optical orthogonal codes with index two. In this paper, we show that there exists a super-simple cyclic ( v , 4 , λ ) for 7 ⩽ v ⩽ 41 and all admissible λ with two definite e...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2007-06, Vol.137 (6), p.2034-2044
Main Authors: Chen, Kejun, Wei, Ruizhong
Format: Article
Language:English
Subjects:
Combinatorics
Combinatorics. Ordered structures
Designs and configurations
Exact sciences and technology
Experimental design
General topics
Mathematics
Optical orthogonal codes
Probability and statistics
Sciences and techniques of general use
Statistics
Super-simple cyclic designs
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Summary:Super-simple cyclic designs are useful on constructing codes and designs such as superimposed codes, perfect hash families and optical orthogonal codes with index two. In this paper, we show that there exists a super-simple cyclic ( v , 4 , λ ) for 7 ⩽ v ⩽ 41 and all admissible λ with two definite exceptions of ( v , λ ) = ( 9 , 3 ) , ( 13 , 5 ) and one possible exception of ( v , λ ) = ( 39 , 18 ) . Some useful algorithms are explained for computer search and new designs are displayed.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2006.04.008