2021 EIMS Intensive Lecture Series
Support t-designs of linear codes
Ewha Institute of Mathematical Sciences (EIMS)
Ewha Womans University, S. Korea, Dec. 1-3, 2021
Abstract
Combinatorial designs and coding theory are closely related. On one hand, a combinatorial design could be used to construct a linear code in different ways. On the other hand, some linear codes could be used to construct exponentially many combinatorial designs. An impressive progress on the construction of t-designs from linear codes has been made in the past six years and several breakthroughs were made recently. In this series of three lectures, we will give a brief introduction to the constructions of t-designs with linear codes and present some open problems on this topic. In Lecture 1, we will introduce support t-designs of codes via the Assumus-Mattson theorem and its generalisation. In Lecture 2, we will cover support t-designs of codes via the automorphism group approach. In Lecture 3, we will talk about the support t-designs of almost MDS and near MDS codes.