Slice cucumber and carrot into thin long strips, sprinkle with salt, and lightly pickle to remove excess moisture.
Drain oil from the canned tuna, then mix with mayonnaise, salt, and pepper.
Place a sheet of seaweed on the sushi mat, and spread rice thinly over it.
Top the rice with cucumber, carrot, and the tuna mixture.
Roll up, then slice into bite-sized pieces.