Infinite Families of Optimal Linear Codes Constructed From Simplicial Complexes
A linear code is optimal if it has the highest minimum distance of any linear code with a given length and dimension. We construct infinite families of optimal binary linear codes <inline-formula> <tex-math notation="LaTeX">C_{\Delta ^{c}} </tex-math></inline-formula&g...
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| Published in: | IEEE transactions on information theory Vol. 66; no. 11; pp. 6762 - 6773 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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IEEE
01.11.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0018-9448, 1557-9654 |
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| Abstract | A linear code is optimal if it has the highest minimum distance of any linear code with a given length and dimension. We construct infinite families of optimal binary linear codes <inline-formula> <tex-math notation="LaTeX">C_{\Delta ^{c}} </tex-math></inline-formula> constructed from simplicial complexes in <inline-formula> <tex-math notation="LaTeX">\mathbb {F}^{n}_{2} </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">\Delta </tex-math></inline-formula> is a simplicial complex in <inline-formula> <tex-math notation="LaTeX">\mathbb {F}^{n}_{2} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\Delta ^{c} </tex-math></inline-formula> the complement of <inline-formula> <tex-math notation="LaTeX">\Delta </tex-math></inline-formula>. We first find an explicit computable criterion for <inline-formula> <tex-math notation="LaTeX">C_{\Delta ^{c}} </tex-math></inline-formula> to be optimal; this criterion is given in terms of the 2-adic valuation of <inline-formula> <tex-math notation="LaTeX">\sum _{i=1}^{s} 2^{|A_{i}|-1} </tex-math></inline-formula>, where the <inline-formula> <tex-math notation="LaTeX">A_{i} </tex-math></inline-formula>'s are maximal elements of <inline-formula> <tex-math notation="LaTeX">\Delta </tex-math></inline-formula>. Furthermore, we obtain much simpler criteria under various specific conditions on the maximal elements of <inline-formula> <tex-math notation="LaTeX">\Delta </tex-math></inline-formula>. In particular, we find that <inline-formula> <tex-math notation="LaTeX">C_{\Delta ^{c}} </tex-math></inline-formula> is a Griesmer code if and only if the maximal elements of <inline-formula> <tex-math notation="LaTeX">\Delta </tex-math></inline-formula> are pairwise disjoint and their sizes are all distinct. Specially, when <inline-formula> <tex-math notation="LaTeX">\mathcal {F} </tex-math></inline-formula> has exactly two maximal elements, we explicitly determine the weight distribution of <inline-formula> <tex-math notation="LaTeX">C_{\Delta ^{c}} </tex-math></inline-formula>. We present many optimal linear codes constructed by our method, and we emphasize that we obtain at least 32 new optimal linear codes. |
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| AbstractList | A linear code is optimal if it has the highest minimum distance of any linear code with a given length and dimension. We construct infinite families of optimal binary linear codes [Formula Omitted] constructed from simplicial complexes in [Formula Omitted], where [Formula Omitted] is a simplicial complex in [Formula Omitted] and [Formula Omitted] the complement of [Formula Omitted]. We first find an explicit computable criterion for [Formula Omitted] to be optimal; this criterion is given in terms of the 2-adic valuation of [Formula Omitted], where the [Formula Omitted]’s are maximal elements of [Formula Omitted]. Furthermore, we obtain much simpler criteria under various specific conditions on the maximal elements of [Formula Omitted]. In particular, we find that [Formula Omitted] is a Griesmer code if and only if the maximal elements of [Formula Omitted] are pairwise disjoint and their sizes are all distinct. Specially, when [Formula Omitted] has exactly two maximal elements, we explicitly determine the weight distribution of [Formula Omitted]. We present many optimal linear codes constructed by our method, and we emphasize that we obtain at least 32 new optimal linear codes. A linear code is optimal if it has the highest minimum distance of any linear code with a given length and dimension. We construct infinite families of optimal binary linear codes <inline-formula> <tex-math notation="LaTeX">C_{\Delta ^{c}} </tex-math></inline-formula> constructed from simplicial complexes in <inline-formula> <tex-math notation="LaTeX">\mathbb {F}^{n}_{2} </tex-math></inline-formula>, where <inline-formula> <tex-math notation="LaTeX">\Delta </tex-math></inline-formula> is a simplicial complex in <inline-formula> <tex-math notation="LaTeX">\mathbb {F}^{n}_{2} </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">\Delta ^{c} </tex-math></inline-formula> the complement of <inline-formula> <tex-math notation="LaTeX">\Delta </tex-math></inline-formula>. We first find an explicit computable criterion for <inline-formula> <tex-math notation="LaTeX">C_{\Delta ^{c}} </tex-math></inline-formula> to be optimal; this criterion is given in terms of the 2-adic valuation of <inline-formula> <tex-math notation="LaTeX">\sum _{i=1}^{s} 2^{|A_{i}|-1} </tex-math></inline-formula>, where the <inline-formula> <tex-math notation="LaTeX">A_{i} </tex-math></inline-formula>'s are maximal elements of <inline-formula> <tex-math notation="LaTeX">\Delta </tex-math></inline-formula>. Furthermore, we obtain much simpler criteria under various specific conditions on the maximal elements of <inline-formula> <tex-math notation="LaTeX">\Delta </tex-math></inline-formula>. In particular, we find that <inline-formula> <tex-math notation="LaTeX">C_{\Delta ^{c}} </tex-math></inline-formula> is a Griesmer code if and only if the maximal elements of <inline-formula> <tex-math notation="LaTeX">\Delta </tex-math></inline-formula> are pairwise disjoint and their sizes are all distinct. Specially, when <inline-formula> <tex-math notation="LaTeX">\mathcal {F} </tex-math></inline-formula> has exactly two maximal elements, we explicitly determine the weight distribution of <inline-formula> <tex-math notation="LaTeX">C_{\Delta ^{c}} </tex-math></inline-formula>. We present many optimal linear codes constructed by our method, and we emphasize that we obtain at least 32 new optimal linear codes. |
| Author | Lee, Yoonjin Lee, Jungyun Hyun, Jong Yoon |
| Author_xml | – sequence: 1 givenname: Jong Yoon orcidid: 0000-0003-2917-5704 surname: Hyun fullname: Hyun, Jong Yoon email: hyun33@kku.ac.kr organization: Konkuk University, Glocal Campus, Chungju, South Korea – sequence: 2 givenname: Jungyun orcidid: 0000-0002-9611-8817 surname: Lee fullname: Lee, Jungyun email: lee9311@kangwon.ac.kr organization: Department of Mathematics Education, Kangwon National University, Chuncheon, South Korea – sequence: 3 givenname: Yoonjin orcidid: 0000-0001-9510-3691 surname: Lee fullname: Lee, Yoonjin email: yoonjinl@ewha.ac.kr organization: Department of Mathematics, Ewha Womans University, Seoul, South Korea |
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| Cites_doi | 10.1007/s00200-016-0292-9 10.1007/s10623-017-0442-5 10.1007/3-540-45066-1_2 10.1109/18.705584 10.1109/TIT.2005.860412 10.1109/LCOMM.2014.2361516 10.1112/blms/18.2.97 10.1145/359168.359176 10.1109/TIT.2015.2473861 10.1016/j.ffa.2015.12.002 10.1109/LCOMM.2015.2455032 10.1109/TIT.2010.2054512 10.1016/S0019-9958(65)90080-X 10.1109/TIT.1979.1056120 10.4169/amer.math.monthly.122.04.367 10.1016/j.disc.2016.03.029 10.1007/978-3-642-45239-0_6 10.1109/MARK.1979.8817296 10.1017/CBO9780511807077 10.1007/s12095-016-0199-0 |
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| References | grassl (ref13) 2020 ref24 ref12 li (ref18) 2016; 27 ref23 ref15 ref14 ref20 ref11 ref10 ref21 blakley (ref4) 1979; 48 adamaszek (ref1) 2015; 122 ref2 macwilliams (ref19) 1977 ref16 huffman (ref17) 2003 xiang (ref22) 2016 ref8 belov (ref3) 1972; 182 ref9 ref6 ref5 cohen (ref7) 2013; 8308 |
| References_xml | – volume: 27 start-page: 481 year: 2016 ident: ref18 article-title: Three classes of binary linear codes with good parameters publication-title: Applicable Algebra Eng Commun Comput doi: 10.1007/s00200-016-0292-9 – ident: ref6 doi: 10.1007/s10623-017-0442-5 – ident: ref12 doi: 10.1007/3-540-45066-1_2 – ident: ref2 doi: 10.1109/18.705584 – ident: ref24 doi: 10.1109/TIT.2005.860412 – ident: ref10 doi: 10.1109/LCOMM.2014.2361516 – year: 2020 ident: ref13 publication-title: Bounds On The Minimum Distance Of Linear Codes And Quantum Codes – ident: ref5 doi: 10.1112/blms/18.2.97 – ident: ref20 doi: 10.1145/359168.359176 – volume: 182 start-page: 100 year: 1972 ident: ref3 article-title: A conjecture on the Griesmer boundary. (Russian) optimization methods and their applications publication-title: All-Union Summer Sem Khakusy Lake Baikal – year: 2016 ident: ref22 article-title: It is indeed a fundamental construction of all linear codes publication-title: arXiv 1610 06355 – ident: ref11 doi: 10.1109/TIT.2015.2473861 – ident: ref16 doi: 10.1016/j.ffa.2015.12.002 – ident: ref15 doi: 10.1109/LCOMM.2015.2455032 – ident: ref8 doi: 10.1109/TIT.2010.2054512 – ident: ref21 doi: 10.1016/S0019-9958(65)90080-X – ident: ref14 doi: 10.1109/TIT.1979.1056120 – volume: 122 start-page: 367 year: 2015 ident: ref1 article-title: Face numbers of down-sets publication-title: Amer Math Monthly doi: 10.4169/amer.math.monthly.122.04.367 – ident: ref9 doi: 10.1016/j.disc.2016.03.029 – volume: 8308 start-page: 85 year: 2013 ident: ref7 article-title: On minimal and quasi-minimal linear codes publication-title: Cryptography and Coding doi: 10.1007/978-3-642-45239-0_6 – volume: 48 start-page: 313 year: 1979 ident: ref4 article-title: Safeguarding cryptographic keys publication-title: International Workshop on Managing Requirements Knowledge (MARK doi: 10.1109/MARK.1979.8817296 – year: 2003 ident: ref17 publication-title: Fundamentals of Error-Correcting Codes doi: 10.1017/CBO9780511807077 – year: 1977 ident: ref19 publication-title: The Theory of Error-Correcting Codes – ident: ref23 doi: 10.1007/s12095-016-0199-0 |
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| SubjectTerms | 3G mobile communication 94A60 Binary codes Binary system Codes Cost accounting Criteria Cryptography Generators Griesmer code Linear codes Mathematics Optimal linear code simplicial complex weight distribution 2010 AMS Subject Classification 94B05 |
| Title | Infinite Families of Optimal Linear Codes Constructed From Simplicial Complexes |
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