The next meeting of the Mathematical Foundations of Informatics seminar will be held on October 31, 2023, at 4 p.m. in Room 578 of the Institute of Mathematics and Informatics.

A talk on:

On binary codes with distances d and d+2

Abstract. In this work, we consider the problem of determining the exact value of $A_2(n, {d, d+2})$ defined as the maximal cardinality of a binary code of length $n$ with two possible distances $d$ and $d+2$. We prove that for fixed even $d$ and $n$ big enough, an optimal code must be a constant-weight code of weight $d/2+1$ with possibly no more than one additional codeword of a different weight.
We also find exact values $A_2(n, {4, 6})$ and $A_2(n, {6, 8})$ starting from some $n$.

This is a joint work with Ivan Landjev.