{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:22:54Z","timestamp":1760242974439,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2015,3,19]],"date-time":"2015-03-19T00:00:00Z","timestamp":1426723200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>An \\(n\\) symbol source which has a Huffman code with codelength vector  \\(L_{n}=(1,2,3,\\cdots,n-2,n-1,n-1)\\) is called an anti-uniform source. In this paper, it is shown that for this class of sources, the optimal fix-free code and symmetric fix-free code is \\(C_{n}^{*}=(0,11,101,1001,\\cdots,1\\overbrace{0\\cdots0}^{n-2}1) \\)<\/jats:p>","DOI":"10.3390\/e17031379","type":"journal-article","created":{"date-parts":[[2015,3,19]],"date-time":"2015-03-19T10:38:57Z","timestamp":1426761537000},"page":"1379-1386","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Optimal Fix-Free Code for Anti-Uniform Sources"],"prefix":"10.3390","volume":"17","author":[{"given":"Ali","family":"Zaghian","sequence":"first","affiliation":[{"name":"Department of Mathematics and Cryptography, Malek Ashtar University of Technology, Isfahan 83145\/115, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Adel","family":"Aghajan","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9919-0323","authenticated-orcid":false,"given":"T.","family":"Gulliver","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Victoria, PO Box 1700, STN CSC, Victoria, BC V8W 2Y2, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,3,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1109\/TIT.1956.1056809","article-title":"On an application of semigroup methods to some problems in coding","volume":"2","year":"1956","journal-title":"IRE Trans. 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