{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:15:36Z","timestamp":1760242536900,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2017,10,22]],"date-time":"2017-10-22T00:00:00Z","timestamp":1508630400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research Foundation of Korea (NRF)","award":["NRF-2015R1D1A1A01060941","NRF- 2014R1A2A2A01006870"],"award-info":[{"award-number":["NRF-2015R1D1A1A01060941","NRF- 2014R1A2A2A01006870"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Fractional repetition (FR) codes are a class of distributed storage codes that replicate and distribute information data over several nodes for easy repair, as well as efficient reconstruction. In this paper, we propose three new constructions of FR codes based on relative difference sets (RDSs) with     \u03bb = 1    . Specifically, we propose new     (  q 2  - 1 , q , q )     FR codes using cyclic RDS with parameters     ( q + 1 , q - 1 , q , 1 )     constructed from q-ary m-sequences of period      q 2  - 1     for a prime power q,     (  p 2  , p , p )     FR codes using non-cyclic RDS with parameters     ( p , p , p , 1 )     for an odd prime p or     p = 4     and     (  4 l  ,  2 l  ,  2 l  )     FR codes using non-cyclic RDS with parameters     (  2 l  ,  2 l  ,  2 l  , 1 )     constructed from the Galois ring for a positive integer l. They are differentiated from the existing FR codes with respect to the constructable code parameters. It turns out that the proposed FR codes are (near) optimal for some parameters in terms of the FR capacity bound. Especially,     ( 8 , 3 , 3 )     and     ( 9 , 3 , 3 )     FR codes are optimal, that is, they meet the FR capacity bound for all k. To support various code parameters, we modify the proposed     (  q 2  - 1 , q , q )     FR codes using decimation by a factor of the code length      q 2  - 1    , which also gives us new good FR codes.<\/jats:p>","DOI":"10.3390\/e19100563","type":"journal-article","created":{"date-parts":[[2017,10,23]],"date-time":"2017-10-23T04:32:19Z","timestamp":1508733139000},"page":"563","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Construction of New Fractional Repetition Codes from Relative Difference Sets with \u03bb=1"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4114-4935","authenticated-orcid":false,"given":"Young-Sik","family":"Kim","sequence":"first","affiliation":[{"name":"Department of Information and Communication Engineering, Chosun University, Gwangju 61452, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7854-7792","authenticated-orcid":false,"given":"Hosung","family":"Park","sequence":"additional","affiliation":[{"name":"School of Electronics and Computer Engineering, Chonnam National University, Gwangju 61186, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jong-Seon","family":"No","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Institute of New Media and Communications, Seoul National University, Seoul 08826, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,10,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4185","DOI":"10.3390\/e16084185","article-title":"Block access token renewal scheme based on secret sharing in Apache Hadoop","volume":"16","author":"Kim","year":"2014","journal-title":"Entropy"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4533","DOI":"10.3390\/e17074533","article-title":"Reliability analysis based on a jump diffusion model with two Wiener processes for cloud computing with big data","volume":"17","author":"Tamura","year":"2015","journal-title":"Entropy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"6925","DOI":"10.1109\/TIT.2012.2208937","article-title":"On the locality of codeword symbols","volume":"58","author":"Gopalan","year":"2012","journal-title":"IEEE Trans. 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