We compute the basic parameters (dimension, length, minimum distance) of affine evaluation codes defined on a cartesian product of finite sets. Given a sequence of positive integers, we construct an evaluation code, over a degenerate torus, with prescribed parameters. As an application of our results, we recover the formulas for the minimum distance of various families of evaluation codes.

A. Samsonov, C. Johnson Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, Utah, United States Introduction: Projections onto convex set (POCS) formalism presents a powerful mathematical apparatus for solving many reconstruction problems that entail incomplete and inconsistent data. Recently, POCS formalism has been adopted for reconstruction of sensitivity encoded ...

We present a cubical type theory based on the Cartesian cube category (faces, degeneracies, symmetries, diagonals, but no connections or reversal) with univalent universes, each containing Π, Σ, path, identity, natural number, boolean, pushout, and glue (equivalence extension) types. The type theory includes a syntactic description of a uniform Kan operation, along with judgemental equality rul...

This note is an illustration of the density-increment method used in the proof of the density Hales-Jewett theorem for k = 3. (Polymath project [2]) I will repeat the argument applying it to a problem which is easier than DHJ. In the last section I will describe the proof of the density Hales-Jewett theorem for k = 3. The results stated here are direct interpretations of the project’s results, ...

This paper presents a new form of Genetic Programming called Cartesian Genetic Programming in which a program is represented as an indexed graph. The graph is encoded in the form of a linear string of integers. The inputs or terminal set and node outputs are numbered sequentially. The node functions are also separately numbered. The genotype is just a list of node connections and functions. The...

The transformation of second-rank Cartesian tensors under rotation plays a fundamental role in the theoretical description of nuclear magnetic resonance experiments, providing the framework for describing anisotropic phenomena such as single crystal rotation patterns, tensor powder patterns, sideband intensities under magic-angle sample spinning, and as input for relaxation theory. Here, two eq...

Traditionally fuzzy controllers have been acquired directly from experts in the field, however recently people have relied upon various learning strategies that automatically acquire such controllers from example data and background knowledge. Here we present a new approach to representing and acquiring controllers based upon Cartesian granule features – multidimensional features formed over th...