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These subgroups can be investigate by means of coding theory as special linear constant weight codes in $\\F_p^{d+1}$. If $p =2$, then the classication of these codes and corresponding lattice polytopes can be obtained using a theorem of Bonisoli. If $p > 2$, the main technical tool in the classification of these linear codes is the non-vanishing theorem for generali"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1309.5312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-09-20T16:30:09Z","cross_cats_sorted":[],"title_canon_sha256":"b3e949cc4e57534b08f63f92acf345e4eea2983ab7b645e9ffd534802c74d090","abstract_canon_sha256":"00b0b83b7b27689437bb76f346acda1ac270d8939a9155ce9d1970ef6b2e175c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:47.032585Z","signature_b64":"xgeSt+xDTvcmN4iXYliDS7lV6C3JgzEm1FfXbU1XG794n9Ebm5Q4YYnnj0ZR/f00Dc5IdGZy0J1lG8viJgDPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af521a9b7a2046993083c153116df0eb1ecdaa489bb7cc10d3101de4f3a8db17","last_reissued_at":"2026-05-18T03:12:47.032037Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:47.032037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lattice polytopes, finite abelian subgroups in $\\SL(n,\\C)$ and coding theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Johannes Hofscheier, Victor Batyrev","submitted_at":"2013-09-20T16:30:09Z","abstract_excerpt":"We consider $d$-dimensional lattice polytopes $\\Delta$ with $h^*$-polynomial $h^*_\\Delta=1+h_k^*t^k$ for $1<k<(d+1)/2$ and relate them to some abelian subgroups of $\\SL_{d+1}(\\C)$ of order $1+h_k^*=p^r$ where $p$ is a prime number. 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