New Bounds on the Size of Permutation Codes With Minimum Kendall $\tau$-distance of Three

Autor:	Abdollahi, A., Bagherian, J., Jafari, F., Khatami, M., Parvaresh, F., Sobhani, R.
Rok vydání:	2022
Předmět:	Mathematics - Combinatorics Mathematics - Group Theory Mathematics - Optimization and Control 94B25 94B65 68P30
Druh dokumentu:	Working Paper
Popis:	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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2206.10193 Zobrazit plný text záznamu View this record from Arxiv