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The flip operation on colored inner-triangle-free triangulations of a convex polygon is studied. It is shown that the affine Weyl group e Cn acts transitively on these triangulations by colored flips, and that the resulting colored flip graph is closely related to a lower interval in the weak order on eCn. Lattice properties of this order are then applied to compute the diameter.

The most common decision criteria for decoding are maximum likelihood decoding and nearest neighbor decoding. It is well-known that maximum likelihood decoding coincides with nearest neighbor decoding with respect to the Hamming metric on the binary symmetric channel. In this work we study channels and metrics for which those two criteria do and do not coincide for general codes.

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We establish the conditions under which it is possible to construct signal sets satisfying the properties of being geometrically uniform and matched to additive quotient groups. Such signal sets consist of subsets of signal spaces identified to integers rings Z[i] and Z[ω] in R 2 .