Dr ALEXANDER KASPRZYK's Outputs (3)

Seven new champion linear codes (2013)
Journal Article
Brown, G., & Kasprzyk, A. M. (2013). Seven new champion linear codes. LMS Journal of Computation and Mathematics, 16, https://doi.org/10.1112/S1461157013000041

We exhibit seven linear codes exceeding the current best known minimum distance d for their dimension k and block length n. Each code is defined over F₈, and their invariants [n,k,d] are given by [49,13,27], [49,14,26], [49,16,24], [49,17,23], [49,19... Read More about Seven new champion linear codes.

Small polygons and toric codes (2013)
Journal Article
Brown, G., & Kasprzyk, A. M. (2013). Small polygons and toric codes. Journal of Symbolic Computation, 51, https://doi.org/10.1016/j.jsc.2012.07.001

We describe two different approaches to making systematic classifications of plane lattice polygons, and recover the toric codes they generate, over small fields, where these match or exceed the best known minimum distance. This includes a [36,19,12]... Read More about Small polygons and toric codes.

Mirror symmetry and Fano manifolds (2013)
Presentation / Conference Contribution
Coates, T., Corti, A., Galkin, S., Golyshev, V., & Kasprzyk, A. M. Mirror symmetry and Fano manifolds. Presented at 6th European Congress of Mathematics

We consider mirror symmetry for Fano manifolds, and describe how one can recover the classification of 3-dimensional Fano manifolds from the study of their mirrors. We sketch a program to classify 4-dimensional Fano manifolds using these ideas.