27th Conference of the International Linear Algebra Society (ILAS 2026)

Code distances: a new family of invariants of linear codes

May 22, 2026, 9:10 AM

25m

Goodwin Hall 125 (Virginia Tech)

Minisymposium Talk Code-based Cryptography Code-based Cryptography

Speaker

Hiram López (Virginia Tech)

Description

We introduce code distances, a new family of invariants for linear codes. We establish some properties and prove bounds on the code distances, and show that they are not invariants of the matroid (for a linear block code) or q-polymatroid (for a rank-metric code) associated to the code. By means of examples, we show that the code distances allow us to distinguish some inequivalent MDS or MRD codes with the same parameters. We also show that no duality holds, i.e., the sequence of code distances of a code does not determine the sequence of code distances of its dual.