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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.

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 $(

Externí odkaz: http://arxiv.org/abs/2206.10193

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Left Dihedral Codes over Finite Chain Rings

Autor: Aghili, H., Sobhani, R.

Let $R$ be a finite commutative chain ring, $D_{2n}$ be the dihedral group of size $2n$ and $R[D_{2n}]$ be the dihedral group ring. In this paper, we completely characterize left ideals of $R[D_{2n}]$ (called left $D_{2n}$-codes) when ${\rm gcd}(char

Externí odkaz: http://arxiv.org/abs/2105.07499

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A conjecture of Cameron and Kiyota on sharp characters with prescribed values

Autor: Abdollahi, A., Bagherian, J., Khatami, M., Shahbazi, Z., Sobhani, R.

Let $ \chi $ be a virtual (generalized) character of a finite group $ G $ and $ L=L(\chi)$ be the image of $ \chi $ on $ G-\lbrace 1 \rbrace $. The pair $ (G, \chi) $ is said to be sharp of type $ L $ if $|G|=\prod _{ l \in L} (\chi(1) - l) $. If the

Externí odkaz: http://arxiv.org/abs/2010.10417

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