Schmidt's conjecture on perfect binary sequences with parameter $d=1$

A perfect binary sequence is a binary periodic sequence of period $n$ with constant periodic autocorrelation at every nonzero shift; $d$ denotes this constant autocorrelation value.

Schmidt's conjecture. There do not exist perfect binary sequences with

$$n>13 \quad\text{and}\quad d=1.$$

The only known perfect binary sequences in this case have $n=5$ and $n=13$, and nonexistence is known for $13<n<20605$. The conjecture remains open beyond the established range.