https://hal.inria.fr/hal-01276485Campello, AntonioAntonioCampelloInstitute of Mathematics, Statistics and Computer Science - UNICAMP - Universidade Estadual de Campinas = University of CampinasVaishampayan, VinayVinayVaishampayanDepartment of Engineering Science and Physics [New York] - CUNY - City University of New York [New York]A Generalization of Montucla's Rectangle-to-Rectangle Dissection to Higher DimensionsHAL CCSD2016DissectionsTilingsLatticesEncodingParameterization[INFO.INFO-IT] Computer Science [cs]/Information Theory [cs.IT]Tillich, Jean-PierrePascale Charpin, Nicolas Sendrier, Jean-Pierre Tillich2016-02-19 14:37:112022-08-05 11:41:042016-02-22 11:17:11enConference papersapplication/pdf1Dissections of polytopes are a well-studied subject by ge-ometers as well as recreational mathematicians. A recent application in coding theory arises from the problem of parameterizing binary vectors of constant Hamming weight [TVS09], [SV09], which is shown to be equivalent to the problem of dissecting a tetrahedron to a brick. An application of dissections to a problem related to the construction of analog codes arises in [CVC13]. Here we consider the rectangle-to-rectangle dissection due to Montu-cla [Fre03]. Montucla's dissection is first reinterpreted in terms of the Two Tile Theorem [SV09]. Based on this, a cube-to-brick dissection is developed in R^n. We present a linear time algorithm (in n) that computes the dissection, i.e. determines a point in the cube given a point in a specific realization of the brick. An application of this algorithm to a previously reported analog coding scheme [CVC13] is also discussed.