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New Bounds on the Size of Permutation Codes With Minimum Kendall $\tau$-distance of Three
- Publication Year :
- 2022
-
Abstract
- We study $P(n,3)$, the size of the largest subset of the set of all permutations $S_n$ with minimum Kendall $\tau$-distance $3$. Using a combination of group theory and integer programming, we reduced the upper bound of $P(p,3)$ from $(p-1)!-1$ to $(p-1)!-\lceil\frac{p}{3}\rceil+2\leq (p-1)!-2$ for all primes $p\geq 11$. In special cases where $n$ is equal to $6,7,11,13,14,15$ and $17$ we reduced the upper bound of $P(n,3)$ by $3,3,9,11,1,1$ and $4$, respectively.
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2206.10193
- Document Type :
- Working Paper