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This master project on algebraic coding theory gathers various techniques from lattice theory, central simple algebras and algebraic number theory. The thesis begins with the formulation of the engineering problem into mathematical form. It presents how sp ...
For the recently proposed model of symbol-pair channels, we advance the pair-error coding theory with algebraic cyclic-code constructions and asymptotic bounds on code rates. Cyclic codes for pair-errors are constructed by a careful use of duals of known t ...
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A Majority-Inverter Graph (MIG) is a homogeneous logic network, where each node represents the majority function. Recently, a logic optimization package based on the MIG data-structure, with 3-input majority node (M3) has been proposed [2], [30]. It is dem ...
This article approaches the incremental view maintenance problem from an algebraic perspective. The algebraic structure of a ring of databases is constructed and extended to form a powerful aggregate query calculus. The query calculus inherits the key prop ...
We consider the initial value problem for the inviscid Primitive and Boussinesq equations in three spatial dimensions. We recast both systems as an abstract Euler-type system and apply the methods of convex integration of De Lellis and Sz,kelyhidi to show ...
Polar codes are constructed for arbitrary channels by imposing an arbitrary quasigroup structure on the input alphabet. The block error probability under successive cancellation decoding decays exponentially with the square root of the block length. It is ...
We prove trace inequalities for a self-adjoint operator on an abstract Hilbert space, which extend those known previously for Laplacians and Schrodinger operators, freeing them from restrictive assumptions on the nature of the spectrum and allowing operato ...
Answering a question posed by Bergelson and Leibman in [6], we establish a nilpotent version of the Polynomial Hales–Jewett Theorem that contains the main theorem in [6] as a special case. Important to the formulation and the proof of our main theorem is t ...
B-series are a fundamental tool in practical and theoretical aspects of numerical integrators for ordinary differential equations. A composition law for B-series permits an elegant derivation of order conditions, and a substitution law gives much insight i ...
