{"paper":{"title":"Some Bounds on Binary LCD Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Byung-Sun Won, Jon-Lark Kim, Lucky Galvez, Nari Lee, Young Gun Roe","submitted_at":"2017-01-16T04:49:33Z","abstract_excerpt":"A linear code with a complementary dual (or LCD code) is defined to be a linear code $C$ whose dual code $C^{\\perp}$ satisfies $C \\cap C^{\\perp}$= $\\left\\{ \\mathbf{0}\\right\\} $. Let $LCD{[}n,k{]}$ denote the maximum of possible values of $d$ among $[n,k,d]$ binary LCD codes. We give exact values of $LCD{[}n,k{]}$ for $1 \\le k \\le n \\le 12$.\n  We also show that $LCD[n,n-i]=2$ for any $i\\geq2$ and $n\\geq2^{i}$. Furthermore, we show that $LCD[n,k]\\leq LCD[n,k-1]$ for $k$ odd and $LCD[n,k]\\leq LCD[n,k-2]$ for $k$ even."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.04165","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"}