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- K. Drakakis, R. Gow, L. O'Carroll
- 2006 40th Annual Conference on Information…
- 2006

We prove that Welch-constructed Costas arrays are in general not symmetric and that the Golomb-constructed ones are symmetric in two cases only, namely the Lem-pel one and a (rare) second one leading to the construction of dense Golomb rulers. Finally, we look into the (hard) problem of the number of fixed points of a Welch-constructed Costas array and… (More)

- Konstantinos Drakakis, Rod Gow, Liam O'Carroll
- Discrete Mathematics
- 2009

We prove that Welch Costas arrays are in general not symmetric and that there exist two special families of symmetric Golomb Costas arrays: one is the well-known Lempel family, while the other, although less well known, leads actually to the construction of dense Golomb rulers.

- Liam O'Carroll, Francesc Planas-Vilanova, Rafael H. Villarreal
- SIAM J. Discrete Math.
- 2014

We study the degree of nonhomogeneous lattice ideals over arbitrary fields, and give formulas to compute the degree in terms of the torsion of certain factor groups of Z s and in terms of relative volumes of lattice polytopes. We also study primary decompositions of lattice ideals over an arbitrary field using the Eisenbud–Sturmfels theory of binomial… (More)

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