{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T21:51:16Z","timestamp":1773352276813,"version":"3.50.1"},"reference-count":24,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,11]],"date-time":"2023-07-11T00:00:00Z","timestamp":1689033600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61701331"],"award-info":[{"award-number":["61701331"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2021YFG0012"],"award-info":[{"award-number":["2021YFG0012"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["XZ202201ZD0006G02"],"award-info":[{"award-number":["XZ202201ZD0006G02"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Sichuan Science and Technology Plan Project","award":["61701331"],"award-info":[{"award-number":["61701331"]}]},{"name":"Sichuan Science and Technology Plan Project","award":["2021YFG0012"],"award-info":[{"award-number":["2021YFG0012"]}]},{"name":"Sichuan Science and Technology Plan Project","award":["XZ202201ZD0006G02"],"award-info":[{"award-number":["XZ202201ZD0006G02"]}]},{"name":"Science and Technology Major Project of Tibetan Autonomous Region of China","award":["61701331"],"award-info":[{"award-number":["61701331"]}]},{"name":"Science and Technology Major Project of Tibetan Autonomous Region of China","award":["2021YFG0012"],"award-info":[{"award-number":["2021YFG0012"]}]},{"name":"Science and Technology Major Project of Tibetan Autonomous Region of China","award":["XZ202201ZD0006G02"],"award-info":[{"award-number":["XZ202201ZD0006G02"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In quasi-synchronous frequency-hopping multiple access (QS-FHMA) systems, low-hit-zone (LHZ) frequency-hopping sequence (FHS) sets have been well-applied to reduce mutual interference (MI). In this paper, we propose three constructions of LHZ FHS sets with new parameters via interleaving techniques. The obtained sequences can be verified that they are optimal with respect to the Peng\u2013Fan\u2013Lee bound.<\/jats:p>","DOI":"10.3390\/e25071044","type":"journal-article","created":{"date-parts":[[2023,7,12]],"date-time":"2023-07-12T00:50:41Z","timestamp":1689123041000},"page":"1044","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Construction of Optimal Frequency Hopping Sequence Set with Low-Hit-Zone"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7154-4879","authenticated-orcid":false,"given":"Xinyu","family":"Tian","sequence":"first","affiliation":[{"name":"College of Computer Science, Sichuan Normal University, Chengdu 610101, China"},{"name":"Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu 610066, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongyu","family":"Han","sequence":"additional","affiliation":[{"name":"College of Computer Science, Sichuan Normal University, Chengdu 610101, China"},{"name":"Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, Chengdu 610066, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xianhua","family":"Niu","sequence":"additional","affiliation":[{"name":"School of Computer and Software Engineering, Xihua University, Chengdu 610039, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0814-8192","authenticated-orcid":false,"given":"Xing","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering, Sichuan University, Chengdu 610065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Golomb, S.W., and Gong, G. (2005). Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar, Cambridge University Press.","DOI":"10.1017\/CBO9780511546907"},{"key":"ref_2","unstructured":"Fan, P., and Darnell, M. (1996). Sequence Design for Communications Applications, Research Studies Press."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1084","DOI":"10.1109\/TCE.2003.1261200","article-title":"A novel family of frequency hopping sequences for multi-hop Bluetooth networks","volume":"49","author":"Li","year":"2003","journal-title":"IEEE Trans. Consum. Electron."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2149","DOI":"10.1109\/TIT.2004.833362","article-title":"Lower bounds on the Hamming auto- and cross correlations of frequency-hopping sequences","volume":"50","author":"Peng","year":"2004","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1007\/s11432-006-0208-6","article-title":"Lower bounds on the periodic Hamming correlations of frequency hopping sequences with low hit zone","volume":"49","author":"Peng","year":"2006","journal-title":"Sci. China Ser. F Inf. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/s10623-010-9422-8","article-title":"New designs of frequency hopping sequences with low hit zone","volume":"60","author":"Ma","year":"2011","journal-title":"Des. Codes Cryptogr."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"5783","DOI":"10.1109\/TIT.2009.2032742","article-title":"New Classes of Optimal Frequency-Hopping Sequences by Interleaving Techniques","volume":"55","author":"Chung","year":"2009","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2207","DOI":"10.1007\/s11432-012-4620-9","article-title":"Frequency\/time hopping sequence sets with optimal partial Hamming correlation properties","volume":"55","author":"Niu","year":"2012","journal-title":"Sci. China Ser. F Inf. Sci."},{"key":"ref_9","first-page":"1835","article-title":"New Classes of Optimal Low Hit Zone Frequency Hopping Sequences with New Parameters","volume":"95","author":"Niu","year":"2014","journal-title":"IEICE Trans. Fundam."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1109\/TIT.2015.2512859","article-title":"Strictly Optimal Frequency-Hopping Sequence Sets With Optimal Family Sizes","volume":"62","author":"Cai","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5782","DOI":"10.1109\/TIT.2014.2332996","article-title":"A New Construction of Frequency-Hopping Sequences With Optimal Partial Hamming Correlation","volume":"60","author":"Cai","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1007\/s12095-016-0192-7","article-title":"New sets of optimal low-hit-zone frequency-hopping sequences based on m-sequences","volume":"9","author":"Han","year":"2017","journal-title":"Cryptogr. Commun."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1142\/S0129054116500040","article-title":"New Constructions of Optimal Frequency-Hopping Sequence Sets with Low-Hit-Zone","volume":"27","author":"Wang","year":"2016","journal-title":"Int. J. Found. Comput. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/s10623-016-0299-z","article-title":"Constructions of optimal low-hit-zone frequency hopping sequence sets","volume":"85","author":"Zhou","year":"2017","journal-title":"Des. Codes Cryptogr.."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1007\/s12095-017-0211-3","article-title":"Generalized methods to construct low-hit-zone frequency-hopping sequence sets and optimal constructions","volume":"9","author":"Zhou","year":"2017","journal-title":"Cryptogr. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2213","DOI":"10.1587\/transfun.E101.A.2213","article-title":"New classes of optimal low hit zone frequency hopping sequence set with large family size","volume":"101","author":"Ling","year":"2018","journal-title":"IEICE Trans. Fundam. Electron. Commun. Comput. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"73870","DOI":"10.1109\/ACCESS.2019.2919353","article-title":"New Extension Interleaved Constructions of Optimal Frequency Hopping Sequence Sets With Low Hit Zone","volume":"7","author":"Niu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"5846","DOI":"10.1109\/TIT.2019.2916362","article-title":"New Extension Constructions of Optimal Frequency-Hopping Sequence Sets","volume":"56","author":"Niu","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Han, H., Zhou, L., and Liu, X. (2019, January 20\u201324). New Construction for Low Hit Zone Frequency Hopping Sequence Sets with Optimal Partial Hamming Correlation. Proceedings of the 2019 Ninth International Workshop on Signal Design and its Applications in Communications (IWSDA), Dongguan, China.","DOI":"10.1109\/IWSDA46143.2019.8966102"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1213","DOI":"10.1109\/TIT.2019.2951383","article-title":"Asymptotic Gilbert\u2013Varshamov Bound on Frequency Hopping Sequences","volume":"66","author":"Niu","year":"2020","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5310","DOI":"10.1109\/TIT.2020.2972388","article-title":"A Construction of Optimal Frequency Hopping Sequence Set via Combination of Multiplicative and Additive Groups of Finite Fields","volume":"66","author":"Niu","year":"2020","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/s12095-021-00518-7","article-title":"Classes of optimal low-hit-zone frequency-hopping sequence sets with new parameters","volume":"14","author":"Zhou","year":"2022","journal-title":"Cryptogr. Commun."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1109\/18.370141","article-title":"Theory and applications of q-ary interleaved sequences","volume":"41","author":"Gong","year":"1995","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2847","DOI":"10.1109\/TIT.2002.804044","article-title":"New designs for signal sets with low cross correlation, balance property, and large linear span: GF(p) case","volume":"48","author":"Gong","year":"2002","journal-title":"IEEE Trans. Inf. Theory"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/7\/1044\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:10:56Z","timestamp":1760127056000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/7\/1044"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,11]]},"references-count":24,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["e25071044"],"URL":"https:\/\/doi.org\/10.3390\/e25071044","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,11]]}}}