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.