Does a person’s fenced backyard, where both ends of the fence connect to the house, have the properties of an eruv? That is to say, may one carry objects within the fence on shabbat?

There are two aspects which need to be considered: 1. Are there any openings in the fence (a gate or just any opening). If there are - as long as they are no wider then 5 meters than there is no problem with carrying objects within the fence. If there are no openings the fence acts as an Eruv. 2. The first aspect is only valid in the case the yard is private. If the yard has more than one owner - one needs to perform an Eruv Chatzerot in which the yard becomes property of both owners together and then both of them can carry in the yard (only if both owners are Jewish!). Rabbi Yosef Weitzen