Computing the Ball Size of Frequency Permutations under Chebyshev Distance

Details Computing the Ball Size of Frequency Permutations under Chebyshev Distance Computing the Ball Size of Frequency Permutations under Chebyshev Distance

2011-02-14

arxiv.org/abs/1102.2799v2

Computer Science

Information Theory

Submitted to ISIT 2011

Scientific paper

Let $S_n^\lambda$ be the set of all permutations over the multiset $\{\overbrace{1,...,1}^{\lambda},...,\overbrace{m,...,m}^\lambda\}$ where $n=m\lambda$. A frequency permutation array (FPA) of minimum distance $d$ is a subset of $S_n^\lambda$ in which every two elements have distance at least $d$. FPAs have many applications related to error correcting codes. In coding theory, the Gilbert-Varshamov bound and the sphere-packing bound are derived from the size of balls of certain radii. We propose two efficient algorithms that compute the ball size of frequency permutations under Chebyshev distance. Both methods extend previous known results. The first one runs in $O({2d\lambda \choose d\lambda}^{2.376}\log n)$ time and $O({2d\lambda \choose d\lambda}^{2})$ space. The second one runs in $O({2d\lambda \choose d\lambda}{d\lambda+\lambda\choose \lambda}\frac{n}{\lambda})$ time and $O({2d\lambda \choose d\lambda})$ space. For small constants $\lambda$ and $d$, both are efficient in time and use constant storage space.

Affiliated with

Also associated with

No associations

Rating

Computing the Ball Size of Frequency Permutations under Chebyshev Distance 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 Computing the Ball Size of Frequency Permutations under Chebyshev Distance, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Computing the Ball Size of Frequency Permutations under Chebyshev Distance will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-216455