{"paper":{"title":"On the nonexistence of $[\\binom{2m}{m-1}, 2m, \\binom{2m-1}{m-1}]$, $m$ odd, complex orthogonal design","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Haibin Kan, Yuan Li","submitted_at":"2011-09-13T19:40:00Z","abstract_excerpt":"Complex orthogonal designs (CODs) are used to construct space-time block codes. 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. Combining with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2891","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}