Complex Hadamard Matrices - a Catalog (since 2006)

@misc{CHM_Catalog,
  author       = {Bruzda, Wojciech and Tadej, Wojciech and \.{Z}yczkowski, Karol},
  title        = {Catalog of Complex Hadamard Matrices},
  howpublished = {\url{https://matrix-toolbox.github.io/chm}},
  year         = {},
  note         = {Accessed: }
}

$F_2^{(0)}$ $= H_2 \supset$ $F_2$ $\in BH(2,2)$ generic and other possible defect values $\in \{0\}$

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$F_3^{(0)}$ $=$ $F_3$ $\in BH(3,3)$$\{0\}$

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$H_4$ $\simeq F_2\otimes F_2\in BH(4,2)$ $\{3\}$

$F_4^{(1)}$ $\supset$ $F_4$ $\in BH(4,4)$ $\{\underline{1}, 3\}$

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$F_5^{(0)}$ $=$ $F_5$ $\in BH(5,5)$$\{0\}$

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$S_6^{(0)}$ $=$ $S_6$ $\in BH(6,3)$ $\{0\}$

$D_6^{(1)}$ $\supset$ $D_6$ $\in BH(6,4)$ $\{\underline{4}\}$

$F_6^{(2)}$ $\supset$ $F_6$ $\simeq F_2\otimes F_3\in BH(6,6),\quad \left(F_6^{(2)}\right)^{\rm T}$ $\{\underline{4}\}$

$B_6^{(1)}$ $\supset$ $C_6^{(0)}$ $\{\underline{4}\}$

$M_6^{(1)}$ $\{\underline{4}\}$

$X_6^{(2)}$ $\{\underline{4}\}$

$K_6^{(2)}$ $\{\underline{4}\}$

$K_6^{(3)}$ $\{\underline{4}\}$

$G_6^{(4)}$ $\{\underline{4}\}$

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$P_7^{(1)}$ $\supset$ $P_7$ $\in BH(7,6)$ $\{\underline{2},3\}$

$F_7^{(0)}$ $=$ $F_7$ $\in BH(7,7)$ $\{0\}$

$C_{7\Sigma \ : \ \Sigma\in\{A,B,C,D\}}^{(0)}$ $\{0\}$

$Q_7^{(0)}$ $\{0\}$

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$D_8^{(4)}$ $\supset$ $H_8$ $\simeq H_2\otimes H_2\otimes H_2\simeq H_4\otimes H_2\in BH(8,2)$ $\{\underline{5}, 7, 9, 15, 21\}$

$S_8^{(4)}$ $\supset$ $S_8$ $\in BH(8,4)$ $\{\underline{5},7,9,11,15,21\}$

$F_2\otimes F_4$ $\in BH(8,4)$$\{13\}$

$F_8^{(5)}$ $\supset$ $F_8$ $\in BH(8,8)$ $\{[\underline{5}, 11], 13\}$

$V_{8\Sigma \ : \ \Sigma\in\{A,B,C,D\}}^{(0)}$ $\{0\}$

$A_8^{(0)}$ $\{0\}$

$T_8^{(1)}$ $\supset \{$ $B_{8A}$, $B_{8B}$ $ \} \subset BH(8,20)$ $\{\underline{3},7,11\}$

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$F_3\otimes F_3$ $\in BH(9,3)$$\{16\}$

$S_9^{(0)}$ $=$ $S_9$ $\in BH(9,6)$$\{0\}$

$F_9^{(4)}$ $\supset$ $F_9$ $\in BH(9,9)$ $\{\underline{4}, 6, 8, 10\}$

$B_9^{(0)}$ $=$ $B_9$ $\in BH(9,10)$$\{2\}$

$N_9^{(0)}$ $\{0\}$

$K_9^{(2)}$ $\{\underline{2},4,10,12,16\}$

$Y_9^{(0)}$ $\{0\}$

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$D_{10}^{(3)}$ $\supset$ $D_{10}$ $\in BH(10,4)$ $\{\underline{9},10,12,16\}$

$X_{10}^{(0)}$ $\in BH(10,5)$$\{0\}$

$S_{10}^{(0)}$ $=$ $S_{10}$ $\in BH(10,5)$ $\{0\}$

$D_{10\Sigma \ : \ \Sigma\in\{A,B\}}^{(7)}$ $\supset$ $\{ D_{10A}, D_{10B} \} \subset BH(10,6)$ $\{\underline{8}_{A,B}, ...\}$

$F_{10}^{(4)}$ $\supset$ $F_{10}$ $\simeq F_2\otimes F_5\in BH(10,10),\quad \left(F_{10}^{(4)}\right)^{\rm T}$ $\{\underline{8}\}$

$N_{10A}$ $\{0\}$

$N_{10B}^{(3)}$ $\{\underline{7},8,10,11\}$

$G_{10}^{(1)}$ $\{8\}$

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$F_{11}^{(0)}$ $=$ $F_{11}$ $\in BH(11,11)$ $\{0\}$

$C_{11\Sigma \ : \ \Sigma\in\{A,B\}}^{(0)}$ $\{0\}$

$N_{11A}^{(0)}$ $\{0\}$

$N_{11B}^{(0)}$ $\{0\}$

$Q_{11\Sigma \ : \ \Sigma\in\{A,B\}}^{(0)}$ $\{0\}$

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$H_{12}^{(7)}$ $\supset$ $H_{12}$ $\in BH(12,2)$ $\{[8, 31], [35, 38], 41, 42, 45, 49, 54, \underline{55}\}$

$X_{12}$ $\in BH(12,3)$$\{12\}$

$D_6\otimes F_2$ $\in BH(12,4)$$\{27\}$

$D_{12}$ $\in BH(12,4)$ $\{45\}$

$F_3\otimes F_2\otimes F_2$ $\simeq F_6\otimes F_2$ $\in BH(12,6)$$\{27\}$

$S_6\otimes F_2$ $\in BH(12,6)$$\{19\}$

$F_{12\Sigma \ : \ \Sigma\in\{A,B,C,D\}}^{(9)}$ $\supset$ $F_{12}$ $\simeq F_3\otimes F_4\in BH(12,12),\quad \left(F_{12\Sigma \ : \ \Sigma\in\{A,B,C,D\}}^{(9)}\right)^{\rm T}$ $\{[\underline{13}_{B,C,D}, 16], [\underline{17}_A, 21], 23\}$

$S_{12}^{(5)}$ $\supset$ $S_{12}$ $\in BH(12,36)$ $\{\underline{11}, 13, 15, 17, 21, 27\}$

$D_{12\Sigma \ : \ \Sigma\in\{A,B,C,...,R\}}^{(9)}$ $\{...\}$

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$M_{13A}$ $\in BH(13,6)$$\{0\}$

$M_{13B}$ $\in BH(13,6)$ $\{\underline{1}, 4\}$

$M_{13C}$ $\in BH(13,6)$ $\{\underline{2}, 3, 4, 6\}$

$F_{13}^{(0)}$ $=$ $F_{13}$ $\in BH(13,13)$ $\{0\}$

$P_{13(A)}^{(4)}$ $\supset$ $P_{13}$ $\in BH(13,60)$ $\{\underline{4},6\}$

$C_{13\Sigma \ : \ \Sigma\in\{A,B\}}^{(0)}$ $\{0\}$

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$D_{14}^{(5)}$ $\supset$ $D_{14}$ $\in BH(14,4)$ $\{[\underline{14},16],[18,20],26,36\}$

$L_{14\Sigma \ : \ \Sigma\in\{A,B,...,N\}}^{(0)}$ $\in BH(14,4)$ $\{0\}$

$P_7\otimes F_2$ $\in BH(14,6)$$\{22\}$

$S_{14}^{(0)}$ $=$ $S_{14}$ $\in BH(14,7)$ $\{0\}$

$L_{14}^{(2)}$ $\in BH(14,10)$$\{10\}$

$F_{14}^{(6)}$ $\supset$ $F_{14}$ $\simeq F_7\otimes F_2\in BH(14,14),\quad \left(F_{14}^{(6)}\right)^{\rm T}$$\{12\}$

$FP_{14}^{(7)}$ $, ...$$\{...\}$

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$F_{15}^{(8)}$ $\supset$ $F_{15}$ $\simeq F_3\otimes F_5\in BH(15,15),\quad \left(F_{15}^{(8)}\right)^{\rm T}$ $\{\underline{16}\}$

$A_{15\Sigma \ : \ \Sigma\in\{A,B,C,...,H\}}$ $\{0,10,16\}$

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$H_{16A}$ $\simeq H_2\otimes H_2\otimes H_2\otimes H_2\in BH(16,2)$$\{105\}$

$H_{16B}$ $\in BH(16,2)$$\{105\}$

$H_{16C}$ $\in BH(16,2)$$\{105\}$

$H_{16D}$ $\in BH(16,2)$$\{105\}$

$H_{16E}$ $\in BH(16,2)$$\{105\}$

$F_4\otimes F_4$ $\in BH(16,4)$$\{57\}$

$S_8\otimes H_2$ $\in BH(16,4)$$\{39\}$

$F_8\otimes H_2$ $\in BH(16,8)$$\{41\}$

$S_{16}^{(11)}$ $\supset$ $S_{16}$ $\in BH(16,8)$ $\{[\underline{12},20], 23,24,27,32,39\}$

$F_{16}^{(17)}$ $\supset$ $F_{16}$ $\in BH(16,16)$ $\{\underline{17}, [19, 27], [29, 32], 34, 36\}$

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$L_{21}^{(0)}$ $\in BH(21,3)$$\{0\}$

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