{"doi":"10.1109/tit.2022.3213568","title":"Orbit Structure of Grassmannian <i>G</i> <sub>2,<i>m</i> </sub> and a Decoder for Grassmann Code <i>C</i> <sub>(2, <i>m</i>)</sub>","abstract":"In this article, we consider decoding Grassmann codes, linear codes associated to the Grassmannian and its embedding in a projective space. We look at the orbit structure of Grassmannian arising from the multiplicative group <inline-formula xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"> <tex-math notation=\"LaTeX\">${\\mathbb {F}}_{q^{m}}^{*}$ </tex-math></inline-formula> in <inline-formula xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"> <tex-math notation=\"LaTeX\">$GL_{m}(q)$ </tex-math></inline-formula> . We project the corresponding Grassmann code onto these orbits to obtain a subcode of a <inline-formula xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"> <tex-math notation=\"LaTeX\">$q$ </tex-math></inline-formula> –ary Reed-Solomon code. We prove that some of these projections contain an information set of the parent Grassmann code. By improving the decoding capacity of Peterson’s decoding algorithm for the projected subcodes, we prove that one can correct up to <inline-formula xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"> <tex-math notation=\"LaTeX\">$\\lfloor (d-1)/2\\rfloor $ </tex-math></inline-formula> errors for Grassmann code, where <inline-formula xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"> <tex-math notation=\"LaTeX\">$d$ </tex-math></inline-formula> is the minimum distance of Grassmann code.","journal":"IEEE Transactions on Information Theory","year":2022,"id":293530,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":1,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9591,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2022-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":978249,"name":"Prasant Singh","orcid":"0000-0003-4400-4858","position":1,"is_corresponding":false},{"id":978248,"name":"Fernando Piñero","orcid":"0000-0002-9714-7249","position":0,"is_corresponding":true}],"reference_count":22,"raw_metadata":null,"created_at":"2026-07-19T00:30:53.818562Z","pmid":"37064162","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}