{"paper":{"title":"A new trace bilinear form on cyclic $\\mathbb{F}_q$-linear $\\mathbb{F}_{q^t}$-codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Fang-Wei Fu, Tingting Wu, Yun Gao","submitted_at":"2016-06-29T14:04:30Z","abstract_excerpt":"Let $\\mathbb{F}_q$ be a finite field of cardinality $q$, where $q$ is a power of a prime number $p$, $t\\geq 2$ an even number satisfying $t \\not\\equiv 1 \\;(\\bmod \\;p)$ and $\\mathbb{F}_{q^t}$ an extension field of $\\mathbb{F}_q$ with degree $t$. First, a new trace bilinear form on $\\mathbb{F}_{{q^t}}^n$ which is called $\\Delta$-bilinear form is given, where $n$ is a positive integer coprime to $q$. Then according to this new trace bilinear form, bases and enumeration of cyclic $\\Delta$-self-orthogonal and cyclic $\\Delta$-self-dual $\\mathbb{F}_q$-linear $\\mathbb{F}_{q^t}$-codes are investigated "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.09106","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"}