American Institute of Mathematical Sciences

Advanced
February  2010, 4(1): 1-22. doi: 10.3934/amc.2010.4.1

On the generalization of the Costas property in higher dimensions

Konstantinos Drakakis 1,

1. 

UCD CASL, University College Dublin, Belfield, Dublin 4

Received  March 2009 Revised  September 2009 Published  February 2010

We investigate the generalization of the Costas property in three or more dimensions, and we seek an appropriate definition; the two main complications are a) that the number of ''dots'' this multidimensional structure should have is not obvious, and b) that the notion of the multidimensional permutation needs some clarification. After proposing various alternatives for the generalization of the definition of the Costas property, based on the definitions of the Costas property in one or two dimensions, we also offer some construction methods, the main one of which is based on the idea of reshaping Costas arrays into higher-dimensional entities.
Keywords: reshaping., hyper-rectangles, Costas property, hypercubes.
Mathematics Subject Classification: Primary: 05B20, 05B35; Secondary: 11B5.
Citation: Konstantinos Drakakis. On the generalization of the Costas property in higher dimensions. Advances in Mathematics of Communications, 2010, 4 (1) : 1-22. doi: 10.3934/amc.2010.4.1
[1]

Konstantinos Drakakis, Scott Rickard. On the generalization of the Costas property in the continuum. Advances in Mathematics of Communications, 2008, 2 (2) : 113-130. doi: 10.3934/amc.2008.2.113
[2]

Jonathan Jedwab, Jane Wodlinger. Structural properties of Costas arrays. Advances in Mathematics of Communications, 2014, 8 (3) : 241-256. doi: 10.3934/amc.2014.8.241
[3]

Konstantinos Drakakis, Roderick Gow, Scott Rickard. Common distance vectors between Costas arrays. Advances in Mathematics of Communications, 2009, 3 (1) : 35-52. doi: 10.3934/amc.2009.3.35
[4]

Konstantinos Drakakis, Francesco Iorio, Scott Rickard, John Walsh. Results of the enumeration of Costas arrays of order 29. Advances in Mathematics of Communications, 2011, 5 (3) : 547-553. doi: 10.3934/amc.2011.5.547
[5]

Konstantinos Drakakis, Francesco Iorio, Scott Rickard. The enumeration of Costas arrays of order 28 and its consequences. Advances in Mathematics of Communications, 2011, 5 (1) : 69-86. doi: 10.3934/amc.2011.5.69
[6]

Konstantinos Drakakis. On the degrees of freedom of Costas permutations and other constraints. Advances in Mathematics of Communications, 2011, 5 (3) : 435-448. doi: 10.3934/amc.2011.5.435
[7]

Joseph H. Silverman. Local-global aspects of (hyper)elliptic curves over (in)finite fields. Advances in Mathematics of Communications, 2010, 4 (2) : 101-114. doi: 10.3934/amc.2010.4.101
[8]

Koray Karabina, Berkant Ustaoglu. Invalid-curve attacks on (hyper)elliptic curve cryptosystems. Advances in Mathematics of Communications, 2010, 4 (3) : 307-321. doi: 10.3934/amc.2010.4.307
[9]

Douglas Hardin, Edward B. Saff, Ruiwen Shu, Eitan Tadmor. Dynamics of particles on a curve with pairwise hyper-singular repulsion. Discrete & Continuous Dynamical Systems, 2021, 41 (12) : 5509-5536. doi: 10.3934/dcds.2021086
[10]

Konstantinos Drakakis, Rod Gow, Scott Rickard. Parity properties of Costas arrays defined via finite fields. Advances in Mathematics of Communications, 2007, 1 (3) : 321-330. doi: 10.3934/amc.2007.1.321
[11]

Bin Han, Changhua Wei. Global well-posedness for inhomogeneous Navier-Stokes equations with logarithmical hyper-dissipation. Discrete & Continuous Dynamical Systems, 2016, 36 (12) : 6921-6941. doi: 10.3934/dcds.2016101
[12]

Kazuhiro Sakai. The oe-property of diffeomorphisms. Discrete & Continuous Dynamical Systems, 1998, 4 (3) : 581-591. doi: 10.3934/dcds.1998.4.581
[13]

Pablo Sánchez, Jaume Sempere. Conflict, private and communal property. Journal of Dynamics & Games, 2016, 3 (4) : 355-369. doi: 10.3934/jdg.2016019
[14]

Kazumine Moriyasu, Kazuhiro Sakai, Kenichiro Yamamoto. Regular maps with the specification property. Discrete & Continuous Dynamical Systems, 2013, 33 (7) : 2991-3009. doi: 10.3934/dcds.2013.33.2991
[15]

Peng Sun. Minimality and gluing orbit property. Discrete & Continuous Dynamical Systems, 2019, 39 (7) : 4041-4056. doi: 10.3934/dcds.2019162
[16]

Bo Su. Doubling property of elliptic equations. Communications on Pure & Applied Analysis, 2008, 7 (1) : 143-147. doi: 10.3934/cpaa.2008.7.143
[17]

Jinjun Li, Min Wu. Generic property of irregular sets in systems satisfying the specification property. Discrete & Continuous Dynamical Systems, 2014, 34 (2) : 635-645. doi: 10.3934/dcds.2014.34.635
[18]

Xuemin Deng, Yuelong Xiao, Aibin Zang. Global well-posedness of the $ n $-dimensional hyper-dissipative Boussinesq system without thermal diffusivity. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1229-1240. doi: 10.3934/cpaa.2021018
[19]

Rafael Potrie. Partially hyperbolic diffeomorphisms with a trapping property. Discrete & Continuous Dynamical Systems, 2015, 35 (10) : 5037-5054. doi: 10.3934/dcds.2015.35.5037
[20]

Björn Gebhard. A note concerning a property of symplectic matrices. Communications on Pure & Applied Analysis, 2018, 17 (5) : 2135-2137. doi: 10.3934/cpaa.2018101

2020 Impact Factor: 0.935

Tools

Metrics

  • PDF downloads (76)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences