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Published at December 5

Recursively Extended Permutation Codes under Chebyshev Distance

cs.IT

math.IT

Released Date: December 5, 2024

Authors: Tomoya Hirobe¹, Kenta Kasai¹

Aff.: ¹Tokyo University

Arxiv: http://arxiv.org/pdf/2412.04148v1

$\underline{\pi}^{(8)}$	$s_{(7)}=$	$\pi_{0}^{(8)}$		$\pi_{1}^{(8)}$		$\pi_{2}^{(8)}$		$\pi_{3}^{(8)}$		$\pi_{4}^{(8)}$		$\pi_{5}^{(8)}$		$\pi_{6}^{(8)}$		$\pi_{7}^{(8)}$
$\uparrow_{7}$			$\nearrow{}^{7}$		$\nearrow{}^{7}$		$\nearrow{}^{7}$		$\nearrow{}^{7}$		$\nearrow{}^{7}$		$\nearrow{}^{7}$		$\nearrow{}^{7}$
$\underline{\pi}^{(7)}$	$s_{(6)}=$	$\pi_{0}^{(7)}$		$\pi_{1}^{(7)}$		$\pi_{2}^{(7)}$		$\pi_{3}^{(7)}$		$\pi_{4}^{(7)}$		$\pi_{5}^{(7)}$		$\pi_{6}^{(7)}$
$\uparrow_{6}$			$\nearrow{}^{6}$		$\nearrow{}^{6}$		$\nearrow{}^{6}$		$\nearrow{}^{6}$		$\nearrow{}^{6}$		$\nearrow{}^{6}$
$\underline{\pi}^{(6)}$	$s_{(5)}=$	$\pi_{0}^{(6)}$		$\pi_{1}^{(6)}$		$\pi_{2}^{(6)}$		$\pi_{3}^{(6)}$		$\pi_{4}^{(6)}$		$\pi_{5}^{(6)}$
$\uparrow_{5}$			$\nearrow{}^{5}$		$\nearrow{}^{5}$		$\nearrow{}^{5}$		$\nearrow{}^{5}$		$\nearrow{}^{5}$
$\underline{\pi}^{(5)}$	$s_{(4)}=$	$\pi_{0}^{(5)}$		$\pi_{1}^{(5)}$		$\pi_{2}^{(5)}$		$\pi_{3}^{(5)}$		$\pi_{4}^{(5)}$
$\uparrow_{4}$			$\nearrow{}^{4}$		$\nearrow{}^{4}$		$\nearrow{}^{4}$		$\nearrow{}^{4}$
$\underline{\pi}^{(4)}$	$s_{(3)}=$	$\pi_{0}^{(4)}$		$\pi_{1}^{(4)}$		$\pi_{2}^{(4)}$		$\pi_{3}^{(4)}$
$\uparrow_{3}$			$\nearrow{}^{3}$		$\nearrow{}^{3}$		$\nearrow{}^{3}$
$\underline{\pi}^{(3)}$	$s_{(2)}=$	$\pi_{0}^{(3)}$		$\pi_{1}^{(3)}$		$\pi_{2}^{(3)}$
$\uparrow_{2}$			$\nearrow{}^{2}$		$\nearrow{}^{2}$
$\underline{\pi}^{(2)}$	$s_{(1)}=$	$\pi_{0}^{(2)}$		$\pi_{1}^{(2)}$
$\uparrow_{1}$			$\nearrow{}^{1}$
$\underline{\pi}^{(1)}$	$s_{(0)}=$	$\pi_{0}^{(1)}$