On Binary Cyclic Codes with Five Nonzero Weights

Computer Science – Information Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Scientific paper

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 \[\sum\limits_{x\in \bF_q}(-1)^{\mathrm{Tr}_1^n(\alpha x^{2^{2k}+1}+\beta x^{2^k+1}+\ga x)}\quad(\alpha,\beta,\ga\in \bF_{q})\] 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 $\pi^{-1}$, $\pi^{-(2^k+1)}$ and $\pi^{-(2^{2k}+1)}$ respectively for a primitive element $\pi$ of $\bF_q$, is also determined.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

On Binary Cyclic Codes with Five Nonzero Weights does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Binary Cyclic Codes with Five Nonzero Weights, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Binary Cyclic Codes with Five Nonzero Weights will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-591575

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.