{"paper":{"title":"On self-dual negacirculant codes of index two and four","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Minjia Shi, Patrick Sole, Qian Liqin","submitted_at":"2017-09-22T00:34:08Z","abstract_excerpt":"In this paper, we study a special kind of factorization of $x^n+1$ over $\\mathbb{F}_q, $ with $q$ a prime power $\\equiv 3~({\\rm mod}~4)$ when $n=2p,$ with $p\\equiv 3~({\\rm mod}~4)$ and $p$ is a prime. Given such a $q$ infinitely many such $p$'s exist that admit $q$ as a primitive root by the Artin conjecture in arithmetic progressions. This number theory conjecture is known to hold under GRH. We study the double (resp. four)-negacirculant codes over finite fields $\\mathbb{F}_q, $ of co-index such $n$'s, including the exact enumeration of the self-dual subclass, and a modified Varshamov-Gilbert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07546","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"}