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Instead of the conventional block-wise inverse Jacket matrix (BIJM), we investigate the cocyclic block-wise inverse Jacket matrix (CBIJM), where the high-order CBIJM can be factorized into the low-order sparse CBIJMs with a successive block architecture. It has a recursive fashion that leads to a fast algorithm concerned for reducing computational load. The fast transforms are also developed for the two-dimensional cocyclic block-wise inverse Jacket transform (CBIJT). The present CBIJM may be used for many matrix-based applications, such as the DFT signal processing, combinatorics, and the Reed-Muller code design.<\/jats:p>\n          <\/jats:sec>","DOI":"10.1186\/1687-6180-2012-184","type":"journal-article","created":{"date-parts":[[2012,8,24]],"date-time":"2012-08-24T08:13:56Z","timestamp":1345796036000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An explicit construction of fast cocyclic jacket transform on the finite field with any size"],"prefix":"10.1186","volume":"2012","author":[{"given":"Ying","family":"Guo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Moon Ho","family":"Lee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kyeong Jin","family":"Kim","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,8,24]]},"reference":[{"key":"343_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-45450-9","volume-title":"Orthogonal Transforms for Digital Signal Processing","author":"NU Ahmed","year":"1975","unstructured":"Ahmed NU, Rao KR: Orthogonal Transforms for Digital Signal Processing. 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