Cyclic Codes and Sequences from a Class of Dembowski-Ostrom 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 $q=p^n$ with $p$ be an odd prime. Let $0\leq k\leq n-1$ and $k\neq n/2$. In this paper we determine the value distribution of following exponential(character) sums \[\sum\limits_{x\in \bF_q}ζ_p^{\Tra_1^n(αx^{p^{3k}+1}+βx^{p^k+1})}\quad(α\in \bF_{p^m},β\in \bF_{q})\] and \[\sum\limits_{x\in \bF_q}ζ_p^{\Tra_1^n(αx^{p^{3k}+1}+βx^{p^k+1}+\ga x)}\quad(α\in \bF_{p^m},β,\ga\in \bF_{q})\] where $\Tra_1^n: \bF_q\ra \bF_p$ and $\Tra_1^m: \bF_{p^m}\ra\bF_p$ are the canonical trace mappings and $ζ_p=e^{\frac{2πi}{p}}$ is a primitive $p$-th root of unity. As applications: (1). We determine the weight distribution of the cyclic codes $\cC_1$ and $\cC_2$ over $\bF_{p^t}$ with parity-check polynomials $h_2(x)h_3(x)$ and $h_1(x)h_2(x)h_3(x)$ respectively where $t$ is a divisor of $d=\gcd(n,k)$, and $h_1(x)$, $h_2(x)$ and $h_3(x)$ are the minimal polynomials of $π^{-1}$, $π^{-(p^k+1)}$ and $π^{-(p^{3k}+1)}$ over $\bF_{p^t}$ respectively for a primitive element $π$ of $\bF_q$. (2). We determine the correlation distribution among a family of m-sequences. | |
| dc.identifier | https://arxiv.org/abs/0902.4509 | |
| dc.identifier | http://arxiv.org/abs/0902.4509 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221595 | |
| dc.subject | Information Theory | |
| dc.subject | Discrete Mathematics | |
| dc.subject | Combinatorics | |
| dc.title | Cyclic Codes and Sequences from a Class of Dembowski-Ostrom Functions | |
| dc.type | text |