9 papers
Large sets of mutually orthogonal quantum Latin squares
Simeon Ball, Robin Simoens
How large can a set of mutually orthogonal quantum Latin squares (MOQLS) get? We show that a set of n - 2 MOQLS of order n is necessarily classical and construct large non-classica…
Mixed-dimensional quantum MacWilliams identity: Bounds for codes and absolutely maximally entangled states in heterogeneous systems
David González-Lociga, Simeon Ball
As emerging quantum architectures evolve into heterogeneous networks combining different physical substrates, such as qubits for logic and higher-dimensional qudits for robust comm…
Thirty-six quantum officers are entangled
Simeon Ball, Robin Simoens
There exist pairs of orthogonal Latin squares of any order n except if n=2 or n=6 [Bose, Shrikhande and Parker, 1960]. In particular, the problem of Euler's thirty-six officers doe…
Error-correcting codes and absolutely maximally entangled states for mixed dimensional Hilbert spaces
Simeon Ball, Raven Zhang
A major difficulty in quantum computation is the ability to implement fault tolerant computations, protecting information against undesired interactions with the environment. Stabi…
Additive codes from linear codes
Simeon Ball, Tabriz Popatia
We introduce two constructions of additive codes over finite fields. Both constructions start with a linear code over a field with elements and give additive codes over the fie…
Ovoids in the cyclic presentation of PG(3,q)
Kanat Abdukhalikov, Simeon Ball, Duy Ho +1
We consider the cyclic presentation of whose points are in the finite field and describe the known ovoids therein. We revisit the set , co…
Griesmer type bounds for additive codes over finite fields, integral and fractional MDS codes
Simeon Ball, Michel Lavrauw, Tabriz Popatia
In this article we prove Griesmer type bounds for additive codes over finite fields. These new bounds give upper bounds on the length of maximum distance separable (MDS) codes, cod…
Practical implementation of geometric quasi-cyclic LDPC codes
Simeon Ball, Tomàs Ortega
We detail for the first time a complete explicit description of the quasi-cyclic structure of all classical finite generalized quadrangles. Using these descriptions we construct fa…
Stabiliser codes over fields of even order
Simeon Ball, Edgar Moreno, Robin Simoens
We prove that the natural isomorphism between GF(2^h) and GF(2)^h induces a bijection between stabiliser codes on n quqits with local dimension q=2^h and binary stabiliser codes on…