Without seeing the females of this cross, in other words, the females hatched with him, there's no way to say for certain that the cross was a sex link cross. Sex linking is mating in a deliberate cross in order to sex the chicks at hatch. If you put a red (gold) rooster over a barred hen, the resultant chicks can be sexed at hatch. The male chicks will have a head spot and will eventually feather out similar to their barred mother, with red-gold leakage, however. The female chicks will not have a head spot but as they age, their all black fuzz will give way to red-gold leakage in the head, neck and breast area, with the red coming from their red father, of course.
For certain, your cockerel is a barred cross of some kind. It is a mix. With precise, it is impossible to say exactly what was crossed to make him.