A CLASS OF p-ARY CYCLIC CODES AND THEIR WEIGHT ENUMERATORS

作者：Yu, Long^*; Liu, Hongwei

来源：Advances in Mathematics of Communications, 2016, 10(2): 437-457.

DOI：10.3934/amc.2016017

• Cyclic code
• exponential sum
• quadratic form
• weight distribution

Let F(p)m be a finite field with p(m) elements, where p is an odd prime, and m is a positive integer. Let h(1) (x) and h(2) (x) be minimal polynomials of -pi(-1) and pi-(pk+1/2) over F-p, respectively, where it is a primitive element of F(p)m, and k is a positive integer such that m/gcd(m,k) >= 3. In [23], Zhou et al. obtained the weight distribution of a class of cyclic codes over F-p with parity-check polynomial h(1)(x)h(2)(x) in the following two cases:
k is even and gcd(m, k) is odd;
m/gcd(m,k) and k/gcd(m, k) are both odd.
In this paper, we further investigate this class of cyclic codes over F-p in other cases. We determine the weight distribution of this class of cyclic codes.

• 出版日期2016-5
• 单位华中师范大学