On Binary Cyclic Codes with Five Nonzero Weights
| dc.creator | Luo, Jinquan | |
| dc.date | 2009-04-15 | |
| dc.date.accessioned | 2026-07-07T13:04:09Z | |
| dc.date.available | 2026-07-07T13:04:09Z | |
| dc.description | Let $q=2^n$, $0\leq k\leq n-1$, $n/\gcd(n,k)$ be odd and $k\neq n/3, 2n/3$. In this paper the value distribution of following exponential sums \[\sum\limits_{x\in \bF_q}(-1)^{\mathrm{Tr}_1^n(αx^{2^{2k}+1}+βx^{2^k+1}+\ga x)}\quad(α,β,\ga\in \bF_{q})\] is determined. As an application, the weight distribution of the binary cyclic code $\cC$, with parity-check polynomial $h_1(x)h_2(x)h_3(x)$ where $h_1(x)$, $h_2(x)$ and $h_3(x)$ are the minimal polynomials of $π^{-1}$, $π^{-(2^k+1)}$ and $π^{-(2^{2k}+1)}$ respectively for a primitive element $π$ of $\bF_q$, is also determined. | |
| dc.identifier | https://arxiv.org/abs/0904.2237 | |
| dc.identifier | http://arxiv.org/abs/0904.2237 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/227062 | |
| dc.subject | Information Theory | |
| dc.subject | Discrete Mathematics | |
| dc.subject | Combinatorics | |
| dc.title | On Binary Cyclic Codes with Five Nonzero Weights | |
| dc.type | text |