The weight distribution of a class of linear codes from perfect nonlinear functions
IEEE Transactions on Information Theory
On the correlation distribution of the Coulter-Matthews decimation
IEEE Transactions on Information Theory
Sums of Gauss sums and weights of irreducible codes
Finite Fields and Their Applications
On the weight distribution of a class of cyclic codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Cyclic codes and sequences: the generalized Kasami case
IEEE Transactions on Information Theory
Explicit evaluation of some exponential sums
Finite Fields and Their Applications
The weight distribution of a class of p-ary cyclic codes
Finite Fields and Their Applications
The weight distribution of a family of reducible cyclic codes
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
| Hi-index | 0.06 |
Let q=p^m where p is an odd prime, m=3, k=1 and gcd(k,m)=1. Let Tr be the trace mapping from F"q to F"p and @z"p=e^2^@p^i^p. In this paper we determine the value distribution of following two kinds of exponential sums@?x@?F"q@g(@ax^p^^^k^+^1+@bx^2)(@a,@b@?F"q) and@?x@?F"q@g(@ax^p^^^k^+^1+@bx^2+@cx)(@a,@b,@c@?F"q), where @g(x)=@z"p^T^r^(^x^) is the canonical additive character of F"q. As an application, we determine the weight distribution of the cyclic codes C"1 and C"2 over F"p with parity-check polynomial h"2(x)h"3(x) and h"1(x)h"2(x)h"3(x), respectively, where h"1(x), h"2(x) and h"3(x) are the minimal polynomials of @p^-^1, @p^-^2 and @p^-^(^p^^^k^+^1^) over F"p, respectively, for a primitive element @p of F"q.