An algebraic method is proposed for selective harmonic elimination PWM (SHEPWM). By
computing its Groebner bases under the pure lexicographic monomial order, the nonlinear …

In this work we analyze the security of cubic cryptographic constructions with respect to rank
weakness. We detail how to extend the big field idea from quadratic to cubic, and show that …

This article aims to explore the bridge between the algebraic structure of a linear code and
the complete decoding process. To this end, we associate a specific binomial ideal …

Unidirectional or one-way relaying, where two wireless nodes, each of which would like to
create an in-formation flow from one node to the other one via a single decode-and-forward …

The label code of a lattice plays a key role in the characterization of the lattice. Every lattice
Λ can be described in terms of a label code L and an orthogonal sublattice Λ′ such that …

We specialize Möller's algorithm to the computation of Gröbner bases related to lattices. We
give the complexity analysis of our algorithm. Then we provide experiments showing that our …

In this paper, by using a relation between binomial ideal and submodules of Z n in, a
submodule associated with the integer programming (IP) problem is defined. By computing …

In this work, two algorithms are developed related to lattice codes. In the first one, an
extended complete Gr\" obner basis is computed for the label code of a lattice. This basis …

The real solutions number of the switching angles for the SHEPWM inverter has been
discussed in this paper. Firstly, the SHEPWM equations were transformed to polynomial …

In this dissertation, we apply various algebraic techniques to: develop some codebased
cryptosystems; break some noncommutative cryptographic protocols; and theoretically …