Packing Costas Arrays
J.H. Dinitz, P.R.J. Ostergard, D.R. Stinson

TL;DR
This paper investigates Costas Latin squares, providing a classification up to order 27, and explores related structures, confirming the conjecture that no such squares exist for odd orders n ≥ 3.
Contribution
It offers a complete classification of Costas Latin squares up to order 27 and verifies the non-existence for odd orders n ≥ 3, introducing related combinatorial structures.
Findings
No Costas Latin squares for odd n ≥ 3 up to order 27
Complete classification of Costas Latin squares up to order 27
Analysis of related structures like near Costas Latin squares
Abstract
A Costas latin square of order n is a set of n disjoint Costas arrays of the same order. Costas latin squares are studied here from a construction as well as a classification point of view. A complete classification is carried out up to order 27. In this range, we verify the conjecture that there is no Costas latin square for any odd order n >= 3. Various other related combinatorial structures are also considered, including near Costas latin squares (which are certain packings of near Costas arrays) and Vatican Costas squares.
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Taxonomy
Topicsgraph theory and CDMA systems · Coding theory and cryptography · Cellular Automata and Applications
