The weight enumerators of several classes of pp-ary cyclic codes

Let pp be an odd prime, and mm and kk be two positive integers with m≥3m≥3. Let h±1(x)h±1(x) and h±t(x)h±t(x) be the minimal polynomials of ±α−1±α−1 and ±α−t±α−t over FpFp, respectively, where αα is a primitive element of FpmFpm. Let C1,−1,±tC1,−1,±t, C±1,t,−tC±1,t,−t and C1,−1,t,−tC1,−1,t,−t be the cyclic codes over FpFp of length pm−1pm−1 with parity-check polynomials h1(x)h−1(x)h±t(x)h1(x)h−1(x)h±t(x), h±1(x)ht(x)h−t(x)h±1(x)ht(x)h−t(x) and h1(x)h−1(x)ht(x)h−t(x)h1(x)h−1(x)ht(x)h−t(x), respectively. This paper determines the weight distributions of the cyclic codes C1,−1,±tC1,−1,±t, C±1,t,−tC±1,t,−t and C1,−1,t,−tC1,−1,t,−t for the parameter tt satisfying some congruence equations.