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On the degrees of freedom of Costas permutations and other constraints
1. | School of Electrical, Electronic & Mechanical Engineering, University College Dublin, Belfield, Dublin 4 |
References:
[1] |
J. K. Beard, Generating Costas Arrays to Order 200, in "Conference on Information Sciences and Systems (CISS) 2006''; availabl online at http://jameskbeard.com/jameskbeard/ |
[2] |
J. K. Beard, Announcement in Conference on Information Sciences and Systems (CISS) 2010. |
[3] |
C. A. Charalambides, "Enumerative Combinatorics,'' Chapman & Hall/CRC, 2002. |
[4] |
J. P. Costas, Medium constraints on sonar design and performance, Technical Report Class 1 Rep. R65EMH33, GE Co., 1965. |
[5] |
J. P. Costas, A study of detection waveforms having nearly ideal range-doppler ambiguity properties, Proc. IEEE, 72 (1984), 996-1009.
doi: 10.1109/PROC.1984.12967. |
[6] |
K. Drakakis, A review of Costas arrays, J. Appl. Math., 2006, 32 pp. |
[7] |
K. Drakakis, A review of the available construction methods for Golomb rulers, Adv. Math. Commun., 3 (2009), 235-250.
doi: 10.3934/amc.2009.3.235. |
[8] |
K. Drakakis, R. Gow and L. O'Carroll, On the symmetry of Welch- and Golomb-constructed Costas arrays, Disc. Math., 309 (2009), 2559-2563.
doi: 10.1016/j.disc.2008.04.058. |
[9] |
K. Drakakis, R. Gow and S. Rickard, On the disjointness of algebraically constructed Costas arrays, J. Algebra Appl., 10 (2011), 219-240.
doi: 10.1142/S0219498811004537. |
[10] |
K. Drakakis, F. Iorio and S. Rickard, The enumeration of Costas arrays of order 28, Adv. Math. Commun., 5 (2011), 69-86.
doi: 10.3934/amc.2011.5.69. |
[11] |
K. Drakakis, F. Iorio, S. Rickard and J. Walsh, Results of the enumeration of Costas arrays of order 29, Adv. Math. Commun., 5 (2011), 547-553. |
[12] |
K. Drakakis, S. Rickard, J. Beard, R. Caballero, F. Iorio, G. O'Brien and J. Walsh, Results of the enumeration of Costas arrays of order 27, IEEE Trans. Inform. Theory, 54 (2008), 4684-4687.
doi: 10.1109/TIT.2008.928979. |
[13] |
S. Golomb, Algebraic constructions for Costas arrays, J. Combin. Theory Ser. A, 37 (1984), 13-21.
doi: 10.1016/0097-3165(84)90015-3. |
[14] |
S. Golomb and G. Gong, The status of Costas arrays, IEEE Trans. Inform. Theory, 53 (2007), 4260-4265.
doi: 10.1109/TIT.2007.907524. |
[15] |
S. Golomb and H. Taylor, Constructions and properties of Costas arrays, Proc. IEEE, 72 (1984), 1143-1163.
doi: 10.1109/PROC.1984.12994. |
[16] |
G. H. Hardy and E. M. Wright, "An Introduction to the Theory of Numbers,'' 6th edition, Clarendon Press, Oxford, 2008. |
[17] |
P. Ribenboim, "The New Book of Prime Number Records,'' 3rd edition, Springer-Verlag, New York, 1995. |
[18] |
J. Silverman, V. Vickers and J. Mooney, On the number of Costas arrays as a function of array size, Proc. IEEE, 76 (1988), 851-853.
doi: 10.1109/5.7156. |
show all references
References:
[1] |
J. K. Beard, Generating Costas Arrays to Order 200, in "Conference on Information Sciences and Systems (CISS) 2006''; availabl online at http://jameskbeard.com/jameskbeard/ |
[2] |
J. K. Beard, Announcement in Conference on Information Sciences and Systems (CISS) 2010. |
[3] |
C. A. Charalambides, "Enumerative Combinatorics,'' Chapman & Hall/CRC, 2002. |
[4] |
J. P. Costas, Medium constraints on sonar design and performance, Technical Report Class 1 Rep. R65EMH33, GE Co., 1965. |
[5] |
J. P. Costas, A study of detection waveforms having nearly ideal range-doppler ambiguity properties, Proc. IEEE, 72 (1984), 996-1009.
doi: 10.1109/PROC.1984.12967. |
[6] |
K. Drakakis, A review of Costas arrays, J. Appl. Math., 2006, 32 pp. |
[7] |
K. Drakakis, A review of the available construction methods for Golomb rulers, Adv. Math. Commun., 3 (2009), 235-250.
doi: 10.3934/amc.2009.3.235. |
[8] |
K. Drakakis, R. Gow and L. O'Carroll, On the symmetry of Welch- and Golomb-constructed Costas arrays, Disc. Math., 309 (2009), 2559-2563.
doi: 10.1016/j.disc.2008.04.058. |
[9] |
K. Drakakis, R. Gow and S. Rickard, On the disjointness of algebraically constructed Costas arrays, J. Algebra Appl., 10 (2011), 219-240.
doi: 10.1142/S0219498811004537. |
[10] |
K. Drakakis, F. Iorio and S. Rickard, The enumeration of Costas arrays of order 28, Adv. Math. Commun., 5 (2011), 69-86.
doi: 10.3934/amc.2011.5.69. |
[11] |
K. Drakakis, F. Iorio, S. Rickard and J. Walsh, Results of the enumeration of Costas arrays of order 29, Adv. Math. Commun., 5 (2011), 547-553. |
[12] |
K. Drakakis, S. Rickard, J. Beard, R. Caballero, F. Iorio, G. O'Brien and J. Walsh, Results of the enumeration of Costas arrays of order 27, IEEE Trans. Inform. Theory, 54 (2008), 4684-4687.
doi: 10.1109/TIT.2008.928979. |
[13] |
S. Golomb, Algebraic constructions for Costas arrays, J. Combin. Theory Ser. A, 37 (1984), 13-21.
doi: 10.1016/0097-3165(84)90015-3. |
[14] |
S. Golomb and G. Gong, The status of Costas arrays, IEEE Trans. Inform. Theory, 53 (2007), 4260-4265.
doi: 10.1109/TIT.2007.907524. |
[15] |
S. Golomb and H. Taylor, Constructions and properties of Costas arrays, Proc. IEEE, 72 (1984), 1143-1163.
doi: 10.1109/PROC.1984.12994. |
[16] |
G. H. Hardy and E. M. Wright, "An Introduction to the Theory of Numbers,'' 6th edition, Clarendon Press, Oxford, 2008. |
[17] |
P. Ribenboim, "The New Book of Prime Number Records,'' 3rd edition, Springer-Verlag, New York, 1995. |
[18] |
J. Silverman, V. Vickers and J. Mooney, On the number of Costas arrays as a function of array size, Proc. IEEE, 76 (1988), 851-853.
doi: 10.1109/5.7156. |
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