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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)
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.
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)