{"paper":{"title":"Classification of the Z2Z4-linear Hadamard codes and their automorphism groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Denis Krotov, Merc\\`e Villanueva","submitted_at":"2014-08-05T23:51:20Z","abstract_excerpt":"A $Z_2Z_4$-linear Hadamard code of length $\\alpha+2\\beta=2^t$ is a binary Hadamard code which is the Gray map image of a $Z_2Z_4$-additive code with $\\alpha$ binary coordinates and $\\beta$ quaternary coordinates. It is known that there are exactly $[(t-1)/2]$ and $[t/2]$ nonequivalent $Z_2Z_4$-linear Hadamard codes of length $2^t$, with $\\alpha=0$ and $\\alpha\\not=0$, respectively, for all $t\\geq 3$. In this paper, it is shown that each $Z_2Z_4$-linear Hadamard code with $\\alpha=0$ is equivalent to a $Z_2Z_4$-linear Hadamard code with $\\alpha\\not=0$; so there are only $[t/2]$ nonequivalent $Z_2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1147","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"}