{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:18:15Z","timestamp":1758824295388,"version":"3.37.3"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61171082","61301137"],"award-info":[{"award-number":["61171082","61301137"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["ZYGX2018040"],"award-info":[{"award-number":["ZYGX2018040"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2018,12]]},"abstract":"<jats:p> Subspace code is very useful in the error correction for random network coding. In this paper, subspace code based on flats in affine space over finite fields is constructed. Sphere-packing bound, Wang\u2013Xing\u2013Safavi-Naini bound, anticode bound, Ahlswede\u2013Aydinian bound and Gilbert\u2013Varshamov bound for the size of code based on flats in affine space over finite fields are provided. Finally, we introduce another method of obtaining the anticode bound for the size of code based on flats in affine space from Erd\u0151s\u2013Ko\u2013Rado theorem. <\/jats:p>","DOI":"10.1142\/s1793830918500787","type":"journal-article","created":{"date-parts":[[2018,9,14]],"date-time":"2018-09-14T02:07:32Z","timestamp":1536890852000},"page":"1850078","source":"Crossref","is-referenced-by-count":2,"title":["Subspace code based on flats in affine space over finite fields"],"prefix":"10.1142","volume":"10","author":[{"given":"Min-Yao","family":"Niu","sequence":"first","affiliation":[{"name":"College of Science, Civil Aviation University of China, Tianjin 300300, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gang","family":"Wang","sequence":"additional","affiliation":[{"name":"Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, P. R. 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