The negative solution to the famous problem of 36 officers of Euler implies that there are no
two orthogonal Latin squares of order six. We show that the problem has a solution …

We show that a relatively simple reasoning using von Neumann entropy inequalities yields a
robust proof of the quantum Singleton bound for quantum error-correcting codes (QECC) …

Let be a prime power and be an integer with. The-Galois hull of classical linear codes is a
generalization of the Euclidean hull and Hermitian hull. We provide a necessary and …

The construction of quantum maximum distance separable (abbreviated to MDS) error-
correcting codes has become one of the major concerns in quantum coding theory. In this …

We construct quantum MDS codes with parameters\! q^ 2+ 1, q^ 2+ 3-2d, d\! _q q 2+ 1, q 2+
3-2 d, dq for all d\leqslant q+ 1 d⩽ q+ 1, d ≠ qd≠ q. These codes are shown to exist by …

We introduce a hierarchy of linear systems for showing that a given subspace of pure
quantum states is entangled (ie, contains no product states). This hierarchy outperforms …

The problem of determining when entanglement is present in a quantum system is one of
the most active areas of research in quantum physics. Depending on the setting at hand …

This is an expository article aiming to introduce the reader to the underlying mathematics
and geometry of quantum error correction. Information stored on quantum particles is subject …

Determining whether a subspace spanned by certain quantum states is entangled and its
entanglement dimensionality remains a fundamental challenge in quantum information …

We prove that there is a Hermitian self-orthogonal-dimensional truncated generalised Reed-
Solomon code of length over if and only if there is a polynomial of degree at most such that …