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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Exhaustive determination of (1023, 511, 255)-cyclic difference sets


Authors: Peter Gaal and Solomon W. Golomb
Journal: Math. Comp. 70 (2001), 357-366
MSC (2000): Primary 05B10, 94A55
Published electronically: March 1, 2000
MathSciNet review: 1680875
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Abstract: An exhaustive search for (1023, 511, 255)-cyclic difference sets has been conducted. A total of 10 non-equivalent (1023, 511, 255)-cyclic difference sets have been found, all of which are members of previously known or conjectured infinite families. A fast and effective autocorrelation test method was utilized that can also facilitate the testing of longer sequences.


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Additional Information

Peter Gaal
Affiliation: Communication Sciences Institute, University of Southern California, Los Angeles, CA 90089-2565, USA
Email: pgaal@qualcomm.com; milly@mizar.usc.edu

Solomon W. Golomb
Affiliation: Communication Sciences Institute, University of Southern California, Los Angeles, CA 90089-2565, USA

DOI: http://dx.doi.org/10.1090/S0025-5718-00-01196-0
PII: S 0025-5718(00)01196-0
Keywords: Cyclic Hadamard matrices, cyclic difference sets, ideal autocorrelation sequences
Received by editor(s): April 21, 1998
Received by editor(s) in revised form: February 11, 1999
Published electronically: March 1, 2000
Article copyright: © Copyright 2000 American Mathematical Society