Algebraic and Combinatorial Quantum Codes - Petr Lisonek

We discuss some algebraic and combinatorial constructions of quantum codes. We give a variant of Construction X (known mainly from the theory of classical linear codes) that produces many new stabilizer quantum error correcting codes of lengths between 50 and 90 that have a higher minimum distance than the currently best known codes. We study entanglement assisted quantum error correcting codes arising from linear cyclic and constacyclic codes and we give an algorithm for an efficient classification of such codes when the number of e-bits is bounded. We study LDPC entanglement assisted quantum codes constructed from incidence matrices of some classes of generalized quadrangles. We give synthetic geometric constructions of counterexamples to the LU-LC Conjecture and we discuss their possible application to synthetic constructions of non-linear quantum gates. This is joint work with Vijaykumar Singh.