This paper is devoted to finding solutions of polynomial equations in roots of unity. It was conjectured by S. Lang and proved by M. Laurent that all such solutions can be described in terms of a finite number of parametric families called maximal torsion cosets. We obtain new explicit upper bounds for the number of maximal torsion cosets on an algebraic subvariety of the complex algebraic n-to...

Let B be the binary two-error-correcting BCH code of length 2" 1 and let B be the extended code of B. We give formal expressions of weight distributions of the cosets of the codes B only depending on m. We can then deduce the weight distributions of the cosets of B. When m is odd, it is well known that there are four distinct weight distributions for the cosets of B . So our main result is abou...

Distributed Video Coding (DVC) is a coding paradigm that gives the decoder the task to exploit the source statistics to achieve efficient compression. Many approaches to the DVC problem have recently appeared in the literature, including the PRISM codec. Instead of encoding the deterministic quantized prediction error residual, PRISM partitions the quantization lattice into cosets and sends the...