Common distance vectors between Costas arrays | Zendy

Konstantinos Drakakis | Zendy; Roderick Gow | Zendy; Scott Rickard | Zendy

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Common distance vectors between Costas arrays

Author(s) -

Konstantinos Drakakis,

Roderick Gow,

Scott Rickard

Publication year - 2009

Publication title -

advances in mathematics of communications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.601

H-Index - 26

eISSN - 1930-5346

pISSN - 1930-5338

DOI - 10.3934/amc.2009.3.35

Subject(s) - mathematics , golomb coding , set (abstract data type) , conjecture , property (philosophy) , combinatorics , vector (molecular biology) , discrete mathematics , computer science , artificial intelligence , image compression , philosophy , recombinant dna , biochemistry , chemistry , epistemology , image (mathematics) , gene , programming language , image processing

We investigate the distance vectors contained in individual Costas arrays and in pairs of Costas arrays, and prove some rigorous results in the case of the algebraically constructed arrays. Overall, it appears that the set with the property that every Costas array has a distance vector in this set, or that every pair of Costas arrays with a common vector have a common vector in this set, is in both cases surprisingly small. Further, we study Costas arrays with the additional property that they represent configurations of non-attacking kings or queens: in the former case, we demonstrate that such arrays are either sporadic or produced by a sub-method of the Lempel construction; in the latter case, partially answering a question asked by S. Golomb 26 years ago, we prove that (non-trivial) such arrays can only be sporadic and conjecture they do not exist at all.

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