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

Let p be an odd prime, and m and k be two positive integers with m >= 3. Let h(+/- 1) (x) and h(+/- t) (x) be the minimal polynomials of +/-alpha(-1) and +/-alpha(-t) over F-p, respectively, where alpha is a primitive element of F-pm. Let C-1,C- -1,C- +/- t, C-+/- 1,C- (t, -t), C-1,C- -1,C- t,C- -t be the cyclic codes over F-p of length p(m) - 1 with parity-check polynomials h(1)(x)h(-1)(x)h(+/- t)(x), h(+/- t)(x)h(t)(x)h(-t)(x) and h(1)(x)h(-1)(x)h(t)(x)h(-t) (x), respectively. This paper determines the weight distributions of the cyclic codes C-1,C- -1,C- +/- t, C-+/- 1,C- t,C- -t and C-1,C- -1,C- t,C- -t for the parameter t satisfying some congruence equations. (C) 2015 Elsevier B.V. All rights reserved.