No they are not.
For something to be infectious it has to be caused by a bug (bacteria, virus or fungus) that can be transmitted from one person to another. Corns on the foot are not caused by an infection so they can not be contagious. You can not pass them onto other people in the family or around swimming pools.
Corns on the foot are caused by too much pressure. They don’t have roots that they grow back from when removed. To treat a corn on the foot, that pressure that causes it needs to be removed.
The myth that corns may be contagious could arise because people get confused between corns and verrucae on the feet. A verruca (wart) is a small skin lesion that is caused by a virus, so can be passed on to other people. They are not corns.
