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Scott Rickard. The quest for Costas arrays. In IEEE AES Regional Meeting, New Jersey, USA, October 2002.
In the 1960’s, Dr. John P. Costas began searching for permutation matrices with ideal auto-ambiguity properties. By hand, he found examples of such matrices of size up to N = 12. Unable to find one of size 13, he contacted Professor Solomon Golomb who then provided generation techniques based on the theory of finite fields for creating these matrices, dubbed Costas arrays. The generation methods produce Costas arrays for infinitely many N, but not all N. For example, the techniques can be used to generate arrays for all N <=31, but no Costas array of size N = 32 or N = 33 has been found. Computer search has enumerated all Costas arrays of size N . 23, but the exponential growth of the search space prohibits extending these results much further with current computational capabilities. After nearly 40 years of research, the first question concerning Costas arrays remains open: Do Costas arrays exist for all N?
@inproceedings{rickard02quest,
AUTHOR = "Scott Rickard",
TITLE = "The quest for Costas arrays",
BOOKTITLE = "IEEE AES Regional Meeting",
abstract = {In the 1960’s, Dr. John P. Costas began searching for permutation matrices
with ideal auto-ambiguity properties. By hand, he found examples of such
matrices of size up to N = 12. Unable to find one of size 13, he contacted
Professor Solomon Golomb who then provided
generation techniques based on the theory
of finite fields for creating these matrices, dubbed
Costas arrays. The generation methods produce
Costas arrays for infinitely many N, but not
all N. For example, the techniques can be used
to generate arrays for all N <=31, but no Costas
array of size N = 32 or N = 33 has been found.
Computer search has enumerated all Costas
arrays of size N . 23, but the exponential
growth of the search space prohibits extending these results much further with
current computational capabilities. After nearly 40 years of research, the first
question concerning Costas arrays remains open:
Do Costas arrays exist for all N? },
ADDRESS= "New Jersey, USA",
YEAR = 2002,
MONTH = oct,
bib2html_pubtype = {Conference Papers},
bib2html_rescat = {Generation Methods},
bib2html_dl_pdf = "http://www.costasarrays.org/costasrefs/rickard02quest.pdf",
}
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