The ideal way to make a longer/wider piece of plywood is to make a scarf joint—basically opposing thin wedges on the two sheets, and glue the long ends of the wedge together. This is fairly common in e.g. boatbuilding where long plywood planks are sometimes needed. Typical slopes for the angles are 9:1 to 12:1 or greater, around 7 to 9" long for 3/4" thick plywood. Cutting such an angle is a bit tricky; a jig of some sort is usually essential. (
Here is an example of a jig design that looks pretty straightforward and effective, using a router for the cutting tool.) Clamping and aligning the joint for gluing can also be somewhat challenging
Done neatly, with good glue, this is every bit as strong as a single sheet of plywood and no heavier. Tightbond III glue would be an acceptable choice and is fairly easy to work with, provided the joint fits tightly everywhere; indeed practically all modern wood glues are stronger than wood when properly applied. Good epoxy (West System is arguably the best, but isn't cheap), with a thickener such as fine sawdust, is probably ideal as it has better gap filling properties and doesn't need to be clamped as tightly.
I would suggest looking for genuine marine plywood, or at the very least exterior plywood. The difference is primarily in the glues used; normal interior plywood doesn't hold up all that well in the presence of moisture.
Have you figured out where the water is getting in? Depending where it is, you may well have damage to the side walls or the front wall as well as the floor. It's obviously foolish to repair the rot without fixing the leak that led to the rot.