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COD $\\mathcal{O}_z$ with parameter $[p, n, k]$ is a $p\\times n$ matrix, where nonzero entries are filled by $\\pm z_i$ or $\\pm z^*_i$, $i = 1, 2,..., k$, such that $\\mathcal{O}^H_z \\mathcal{O}_z = (|z_1|^2+|z_2|^2+...+|z_k|^2)I_{n \\times n}$. Adams et al. in \"The final case of the decoding delay problem for maximum rate complex orthogonal designs,\" IEEE Trans. Inf. Theory, vol. 56, no. 1, pp. 103-122, Jan. 2010, first proved the nonexistence of $[\\binom{2m}{m-1}, 2m, \\binom{2m-1}{m-1}]$, $m$ odd, COD. 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COD $\\mathcal{O}_z$ with parameter $[p, n, k]$ is a $p\\times n$ matrix, where nonzero entries are filled by $\\pm z_i$ or $\\pm z^*_i$, $i = 1, 2,..., k$, such that $\\mathcal{O}^H_z \\mathcal{O}_z = (|z_1|^2+|z_2|^2+...+|z_k|^2)I_{n \\times n}$. Adams et al. in \"The final case of the decoding delay problem for maximum rate complex orthogonal designs,\" IEEE Trans. Inf. Theory, vol. 56, no. 1, pp. 103-122, Jan. 2010, first proved the nonexistence of $[\\binom{2m}{m-1}, 2m, \\binom{2m-1}{m-1}]$, $m$ odd, COD. 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