{"paper":{"title":"All binary linear codes that are invariant under $\\PSL_2(n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Cunsheng Ding, Hao Liu, Vladimir D. Tonchev","submitted_at":"2017-04-04T21:50:27Z","abstract_excerpt":"The projective special linear group $\\PSL_2(n)$ is $2$-transitive for all primes $n$ and $3$-homogeneous for $n \\equiv 3 \\pmod{4}$ on the set $\\{0,1, \\cdots, n-1, \\infty\\}$. It is known that the extended odd-like quadratic residue codes are invariant under $\\PSL_2(n)$. Hence, the extended quadratic residue codes hold an infinite family of $2$-designs for primes $n \\equiv 1 \\pmod{4}$, an infinite family of $3$-designs for primes $n \\equiv 3 \\pmod{4}$. To construct more $t$-designs with $t \\in \\{2, 3\\}$, one would search for other extended cyclic codes over finite fields that are invariant under"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01199","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"}