Abstract: Let be a polynomial of degree less than over a finite field . Its value at any given point in can be found once we know its values at any other points . We consider the problem of finding by observing some partial information about the values of at points, i.e., some functions . We present a construction that gives an optimal solution of this problem (we will discuss the meaning of optimality along the way). The construction relies on specially designed subfields of . This problem is known in coding theory as the repair problem of Reed-Solomon codes, and we will use coding theoretic language in the description of the solution. Based on recent joint works with Itzhak Tamo and Min Ye.
