Erasure List-Decodable Codes From Random and Algebraic Geometry Codes

List-decodable zero-rate codes

We consider list-decoding in the zero-rate regime for two cases: the binary alphabet and the spherical codes in Euclidean space. Specifically, we study the maximal τ ∈ [0, 1] for which there exists an arrangement ofM balls of relative Hamming radius τ in the binary hypercube (of arbitrary dimension) with the property that no point of the latter is covered by L or more of them. As M →∞ the maxim...

Quantum Codes from Algebraic Geometry

Quantum error correcting codes are essential for successful implementation of quantum computers. We look into the theory of a particular class of quantum codes that look promising called quantum stabilizer codes. The aim of this project is to study and construct efficient quantum stabilizer codes from algebraic geometry codes.

On Fast-Decodable Algebraic Space-Time Codes

In the near future, the 5th generation (5G) wireless systems will be established. They will consist of an integration of different techniques, including distributed antenna systems and massive multiple-input multiple-output systems, and the overall performance will highly depend on the channel coding techniques employed. Due to the nature of future wireless networks, space– time codes are no lo...

Algebraic Geometry Codes

Algebraic-Geometry Codes