{"paper":{"title":"Complex Orthogonal Designs with Forbidden $2 \\times 2$ Submatrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.IT"],"primary_cat":"cs.IT","authors_text":"Haibin Kan, Yuan Li","submitted_at":"2011-07-17T01:18:46Z","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 $\\mathcal{O}^H_z \\mathcal{O}_z = (|z_1|^2+|z_2|^2+...+|z_k|^2)I_{n \\times n}$. Define $\\mathcal{O}_z$ a first type COD if and only if $\\mathcal{O}_z$ does not contain submatrix {\\pm z_j & 0; \\ 0 & \\pm z^*_j}$ or ${\\pm z^*_j & 0; \\ 0 & \\pm z_j}$. It is already known that, all CODs with maximal rate, i.e., maximal $k/p$, are of the first type.\n  In this pa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3268","kind":"arxiv","version":2},"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"}