2 REMARKS ON A PAPER BY MORENO AND KUMAR

In a recent article O. Moreno and P. V. Kumar showed how Deligne's the orem can be applied to coding theory. They studied certain subcodes of binary Reed-Muller codes and estimated the associated character sums over a held of q(2) elements. They obtained bounds of the order O (q). In this correspondence we show that in one case we can improve the co efficient of q in the estimates. We also show that there is an error i n Moreno and Kumar's argument and in some cases rye need to replace a bound of the order O (q) by a weaker bound of the order O (q(3/2)).