1 research outputs found
Cyclic Codes and Sequences from Kasami-Welch Functions
Let , and . In this paper we determine
the value distribution of following exponential sums \sum\limits_{x\in
\bF_q}(-1)^{\Tra_1^n(\alpha x^{2^{3k}+1}+\beta x^{2^k+1})}\quad(\alpha,\beta\in
\bF_{q}) and \sum\limits_{x\in \bF_q}(-1)^{\Tra_1^n(\alpha
x^{2^{3k}+1}+\beta x^{2^k+1}+\ga x)}\quad(\alpha,\beta,\ga\in \bF_{q}) where
\Tra_1^n: \bF_{2^n}\ra \bF_2 is the canonical trace mapping. As applications:
(1). We determine the weight distribution of the binary cyclic codes \cC_1
and \cC_2 with parity-check polynomials and
respectively where , and are the
minimal polynomials of , and
respectively for a primitive element of \bF_q. (2). We determine the
correlation distribution among a family of binary m-sequences