Several new classes of linear codes with few weights

Let ?q be a finite field of order q, where q = p(s) is a power of a prime number p. Let m and m(1) be two positive integers such that m(1) divides m. For any positive divisor e of q -1, we construct an infinite family of codes with dimension m + m(1) and few weights over ?q. Using Gauss sum, their weight distributions are provided. When gcd(e, m) =1, we obtain a subclass of optimal codes which attain the Griesmer bound. Moreover, when gcd(e, m) =2 or 3 we construct new infinite families of codes with at most four weights.