Cyclic Codes and Sequences from Kasami-Welch Functions
| dc.creator | Luo, Jinquan | |
| dc.creator | Ling, San | |
| dc.creator | Xing, Chaoping | |
| dc.date | 2009-02-26 | |
| dc.date.accessioned | 2026-07-07T12:47:05Z | |
| dc.date.available | 2026-07-07T12:47:05Z | |
| dc.description | Let $q=2^n$, $0\leq k\leq n-1$ and $k\neq n/2$. In this paper we determine the value distribution of following exponential sums \[\sum\limits_{x\in \bF_q}(-1)^{\Tra_1^n(αx^{2^{3k}+1}+βx^{2^k+1})}\quad(α,β\in \bF_{q})\] and \[\sum\limits_{x\in \bF_q}(-1)^{\Tra_1^n(αx^{2^{3k}+1}+βx^{2^k+1}+\ga x)}\quad(α,β,\ga\in \bF_{q})\] 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 $h_2(x)h_3(x)$ 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 $π^{-1}$, $π^{-(2^k+1)}$ and $π^{-(2^{3k}+1)}$ respectively for a primitive element $π$ of $\bF_q$. (2). We determine the correlation distribution among a family of binary m-sequences. | |
| dc.identifier | https://arxiv.org/abs/0902.4511 | |
| dc.identifier | http://arxiv.org/abs/0902.4511 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221597 | |
| dc.subject | Information Theory | |
| dc.subject | Discrete Mathematics | |
| dc.subject | Combinatorics | |
| dc.title | Cyclic Codes and Sequences from Kasami-Welch Functions | |
| dc.type | text |