ieee-ABJKPS-12-June-2022.pdf (101.78 kB)

Download file# New Bounds on the Size of Permutation Codes With Minimum Kendall T-distance of Three

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.

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## Email Address of Submitting Author

a.abdollahi@math.ui.ac.ir## ORCID of Submitting Author

0000-0001-7277-4855## Submitting Author's Institution

University of Isfahan## Submitting Author's Country

- Iran