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The enumeration of Costas arrays of order 28 and its consequences
1. | School of Electrical, Electronic & Mechanical Engineering, University College Dublin, Belfield, Dublin 4 |
2. | Autodesk Research, 210 King Street East, Toronto, Ontario M5A 1J7, Canada |
References:
[1] |
L. Barker, K. Drakakis and S. Rickard, On the complexity of the verification of the Costas property, Proc. IEEE, 97 (2009), 586-593.
doi: 10.1109/JPROC.2008.2011947. |
[2] | |
[3] |
J. K. Beard, J. C. Russo, K. G. Erickson, M. C. Monteleone and M. T. Wright, Costas arrays generation and search methodology, IEEE Trans. Aerospace Electr. Systems, 43 (2007), 522-538.
doi: 10.1109/TAES.2007.4285351. |
[4] |
C. Brown, M. Cenki, R. Games, J. Rushanan, O. Moreno and P. Pei, New enumeration results for Costas arrays, in "IEEE International Symposium on Information Theory,'' (1993), 405.
doi: 10.1109/ISIT.1993.748721. |
[5] |
S. Cohen and G. Mullen, Primitive elements in finite fields and Costas arrays, Appl. Algebra Engin. Commun. Comput., 2 (1991), 45-53.
doi: 10.1007/BF01810854. |
[6] |
J. P. Costas, Medium constraints on SONAR design and performance, in "Technical Report Class 1 Rep. R65EMH33,'' GE Co., 1965; A synopsis of this report appeared in the EASCON Convention Record, (1975), 68A-68L. |
[7] |
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. |
[8] |
K. Drakakis, A review of Costas arrays, J. Appl. Math., 2006, 32. |
[9] |
K. Drakakis, R. Gow and L. O'Carroll, On the symmetry of Welch- and Golomb-constructed Costas arrays, Discrete Math., 309 (2009), 2559-2563.
doi: 10.1016/j.disc.2008.04.058. |
[10] |
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. |
[11] |
S. W. Golomb, Algebraic constructions for Costas arrays, J. Combin. Theory Ser. A, 37 (1984), 13-21.
doi: 10.1016/0097-3165(84)90015-3. |
[12] |
S. W. Golomb, The $T_4$ and $G_4$ constructions for Costas arrays, IEEE Trans. Inform. Theory, 38 (1992), 1404-1406.
doi: 10.1109/18.144726. |
[13] |
S. W. Golomb and H. Taylor, Constructions and properties of Costas arrays, Proc. IEEE, 72 (1984), 1143-1163.
doi: 10.1109/PROC.1984.12994. |
[14] |
K. Ireland and M. Rosen, "A Classical Introduction to Modern Number Theory,'' $2^{nd}$ edition, Springer, 1990. |
[15] |
S. Rickard, Searching for Costas arrays using periodicity properties, in "IMA International Conference on Mathematics in Signal Processing at The Royal Agricultural College,'' Cirencester, UK, 2004. |
[16] |
S. Rickard, Open problems in Costas arrays, in "IMA International Conference on Mathematics in Signal Processing at The Royal Agricultural College,'' Cirencester, UK, 2006. |
[17] |
S. Rickard, E. Connell, F. Duignan, B. Ladendorf and A. Wade, The enumeration of Costas arrays of size 26, in "Conference on Information Signals and Systems,'' Princeton University, USA, 2006.
doi: 10.1109/CISS.2006.286579. |
[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. |
[19] |
K. Taylor, K. Drakakis and S. Rickard, Generated, emergent, and sporadic Costas arrays, in "IMA International Conference on Mathematics in Signal Processing at The Royal Agricultural College,'' Cirencester, UK, 2008. |
show all references
References:
[1] |
L. Barker, K. Drakakis and S. Rickard, On the complexity of the verification of the Costas property, Proc. IEEE, 97 (2009), 586-593.
doi: 10.1109/JPROC.2008.2011947. |
[2] | |
[3] |
J. K. Beard, J. C. Russo, K. G. Erickson, M. C. Monteleone and M. T. Wright, Costas arrays generation and search methodology, IEEE Trans. Aerospace Electr. Systems, 43 (2007), 522-538.
doi: 10.1109/TAES.2007.4285351. |
[4] |
C. Brown, M. Cenki, R. Games, J. Rushanan, O. Moreno and P. Pei, New enumeration results for Costas arrays, in "IEEE International Symposium on Information Theory,'' (1993), 405.
doi: 10.1109/ISIT.1993.748721. |
[5] |
S. Cohen and G. Mullen, Primitive elements in finite fields and Costas arrays, Appl. Algebra Engin. Commun. Comput., 2 (1991), 45-53.
doi: 10.1007/BF01810854. |
[6] |
J. P. Costas, Medium constraints on SONAR design and performance, in "Technical Report Class 1 Rep. R65EMH33,'' GE Co., 1965; A synopsis of this report appeared in the EASCON Convention Record, (1975), 68A-68L. |
[7] |
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. |
[8] |
K. Drakakis, A review of Costas arrays, J. Appl. Math., 2006, 32. |
[9] |
K. Drakakis, R. Gow and L. O'Carroll, On the symmetry of Welch- and Golomb-constructed Costas arrays, Discrete Math., 309 (2009), 2559-2563.
doi: 10.1016/j.disc.2008.04.058. |
[10] |
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. |
[11] |
S. W. Golomb, Algebraic constructions for Costas arrays, J. Combin. Theory Ser. A, 37 (1984), 13-21.
doi: 10.1016/0097-3165(84)90015-3. |
[12] |
S. W. Golomb, The $T_4$ and $G_4$ constructions for Costas arrays, IEEE Trans. Inform. Theory, 38 (1992), 1404-1406.
doi: 10.1109/18.144726. |
[13] |
S. W. Golomb and H. Taylor, Constructions and properties of Costas arrays, Proc. IEEE, 72 (1984), 1143-1163.
doi: 10.1109/PROC.1984.12994. |
[14] |
K. Ireland and M. Rosen, "A Classical Introduction to Modern Number Theory,'' $2^{nd}$ edition, Springer, 1990. |
[15] |
S. Rickard, Searching for Costas arrays using periodicity properties, in "IMA International Conference on Mathematics in Signal Processing at The Royal Agricultural College,'' Cirencester, UK, 2004. |
[16] |
S. Rickard, Open problems in Costas arrays, in "IMA International Conference on Mathematics in Signal Processing at The Royal Agricultural College,'' Cirencester, UK, 2006. |
[17] |
S. Rickard, E. Connell, F. Duignan, B. Ladendorf and A. Wade, The enumeration of Costas arrays of size 26, in "Conference on Information Signals and Systems,'' Princeton University, USA, 2006.
doi: 10.1109/CISS.2006.286579. |
[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. |
[19] |
K. Taylor, K. Drakakis and S. Rickard, Generated, emergent, and sporadic Costas arrays, in "IMA International Conference on Mathematics in Signal Processing at The Royal Agricultural College,'' Cirencester, UK, 2008. |
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