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Construction-D lattice from Garcia–Stichtenoth tower code
We show an explicit construction of an efficiently decodable family of n -dimensional lattices whose minimum distances achieve Ω ( n / ( log n ) ε + o ( 1 ) ) for ε > 0 . It improves upon the state-of-the-art construction due to Mook–Peikert (IEEE Trans Inf Theory 68(2):863–870, 2022) that provid...
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| Published in: | Designs, codes, and cryptography codes, and cryptography, 2024-05, Vol.92 (5), p.1127-1142 |
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| Main Authors: | , |
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| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c270t-6038750455dc400ebcfc12c97d720431a64da7b88c178850cf4e682f042413683 |
| container_end_page | 1142 |
| container_issue | 5 |
| container_start_page | 1127 |
| container_title | Designs, codes, and cryptography |
| container_volume | 92 |
| creator | Kirshanova, Elena Malygina, Ekaterina |
| description | We show an explicit construction of an efficiently decodable family of
n
-dimensional lattices whose minimum distances achieve
Ω
(
n
/
(
log
n
)
ε
+
o
(
1
)
)
for
ε
>
0
. It improves upon the state-of-the-art construction due to Mook–Peikert (IEEE Trans Inf Theory 68(2):863–870, 2022) that provides lattices with minimum distances
Ω
(
n
/
log
n
)
. These lattices are construction-D lattices built from a sequence of BCH codes. We show that replacing BCH codes with subfield subcodes of Garcia–Stichtenoth tower codes leads to a better minimum distance. To argue on decodability of the construction, we adapt soft-decision decoding techniques of Koetter–Vardy (IEEE Trans Inf Theory 49(11):2809–2825, 2003) to algebraic-geometric codes. |
| doi_str_mv | 10.1007/s10623-023-01333-2 |
| format | article |
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n
-dimensional lattices whose minimum distances achieve
Ω
(
n
/
(
log
n
)
ε
+
o
(
1
)
)
for
ε
>
0
. It improves upon the state-of-the-art construction due to Mook–Peikert (IEEE Trans Inf Theory 68(2):863–870, 2022) that provides lattices with minimum distances
Ω
(
n
/
log
n
)
. These lattices are construction-D lattices built from a sequence of BCH codes. We show that replacing BCH codes with subfield subcodes of Garcia–Stichtenoth tower codes leads to a better minimum distance. To argue on decodability of the construction, we adapt soft-decision decoding techniques of Koetter–Vardy (IEEE Trans Inf Theory 49(11):2809–2825, 2003) to algebraic-geometric codes.</description><identifier>ISSN: 0925-1022</identifier><identifier>EISSN: 1573-7586</identifier><identifier>DOI: 10.1007/s10623-023-01333-2</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>BCH codes ; Coding and Information Theory ; Computer Science ; Cryptology ; Discrete Mathematics in Computer Science ; Lattices ; Soft decision decoding</subject><ispartof>Designs, codes, and cryptography, 2024-05, Vol.92 (5), p.1127-1142</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-6038750455dc400ebcfc12c97d720431a64da7b88c178850cf4e682f042413683</cites><orcidid>0000-0001-8924-7605 ; 0000-0003-0977-5999</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Kirshanova, Elena</creatorcontrib><creatorcontrib>Malygina, Ekaterina</creatorcontrib><title>Construction-D lattice from Garcia–Stichtenoth tower code</title><title>Designs, codes, and cryptography</title><addtitle>Des. Codes Cryptogr</addtitle><description>We show an explicit construction of an efficiently decodable family of
n
-dimensional lattices whose minimum distances achieve
Ω
(
n
/
(
log
n
)
ε
+
o
(
1
)
)
for
ε
>
0
. It improves upon the state-of-the-art construction due to Mook–Peikert (IEEE Trans Inf Theory 68(2):863–870, 2022) that provides lattices with minimum distances
Ω
(
n
/
log
n
)
. These lattices are construction-D lattices built from a sequence of BCH codes. We show that replacing BCH codes with subfield subcodes of Garcia–Stichtenoth tower codes leads to a better minimum distance. To argue on decodability of the construction, we adapt soft-decision decoding techniques of Koetter–Vardy (IEEE Trans Inf Theory 49(11):2809–2825, 2003) to algebraic-geometric codes.</description><subject>BCH codes</subject><subject>Coding and Information Theory</subject><subject>Computer Science</subject><subject>Cryptology</subject><subject>Discrete Mathematics in Computer Science</subject><subject>Lattices</subject><subject>Soft decision decoding</subject><issn>0925-1022</issn><issn>1573-7586</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kM1KAzEUhYMoWKsv4GrAdfTmP8WVVFuFggt1HdJMxk5pJzVJEXe-g2_ok5hhBHcuDhcu3zmXexA6J3BJANRVIiApw9CLMMYwPUAjIhTDSmh5iEYwoQIToPQYnaS0BigY0BG6noYu5bh3uQ0dvq02NufW-aqJYVvNbXSt_f78eiq7VfZdyKsqh3cfKxdqf4qOGrtJ_ux3jtHL7O55eo8Xj_OH6c0CO6ogYwlMKwFciNpxAL90jSPUTVStKHBGrOS1VUutHVFaC3AN91LTBjjlhEnNxuhiyN3F8Lb3KZt12MeunDQMRPmZMCELRQfKxZBS9I3ZxXZr44chYPqSzFCSgV59SYYWExtMqcDdq49_0f-4fgBwimiy</recordid><startdate>20240501</startdate><enddate>20240501</enddate><creator>Kirshanova, Elena</creator><creator>Malygina, Ekaterina</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-8924-7605</orcidid><orcidid>https://orcid.org/0000-0003-0977-5999</orcidid></search><sort><creationdate>20240501</creationdate><title>Construction-D lattice from Garcia–Stichtenoth tower code</title><author>Kirshanova, Elena ; Malygina, Ekaterina</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-6038750455dc400ebcfc12c97d720431a64da7b88c178850cf4e682f042413683</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>BCH codes</topic><topic>Coding and Information Theory</topic><topic>Computer Science</topic><topic>Cryptology</topic><topic>Discrete Mathematics in Computer Science</topic><topic>Lattices</topic><topic>Soft decision decoding</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kirshanova, Elena</creatorcontrib><creatorcontrib>Malygina, Ekaterina</creatorcontrib><collection>CrossRef</collection><jtitle>Designs, codes, and cryptography</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kirshanova, Elena</au><au>Malygina, Ekaterina</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Construction-D lattice from Garcia–Stichtenoth tower code</atitle><jtitle>Designs, codes, and cryptography</jtitle><stitle>Des. Codes Cryptogr</stitle><date>2024-05-01</date><risdate>2024</risdate><volume>92</volume><issue>5</issue><spage>1127</spage><epage>1142</epage><pages>1127-1142</pages><issn>0925-1022</issn><eissn>1573-7586</eissn><abstract>We show an explicit construction of an efficiently decodable family of
n
-dimensional lattices whose minimum distances achieve
Ω
(
n
/
(
log
n
)
ε
+
o
(
1
)
)
for
ε
>
0
. It improves upon the state-of-the-art construction due to Mook–Peikert (IEEE Trans Inf Theory 68(2):863–870, 2022) that provides lattices with minimum distances
Ω
(
n
/
log
n
)
. These lattices are construction-D lattices built from a sequence of BCH codes. We show that replacing BCH codes with subfield subcodes of Garcia–Stichtenoth tower codes leads to a better minimum distance. To argue on decodability of the construction, we adapt soft-decision decoding techniques of Koetter–Vardy (IEEE Trans Inf Theory 49(11):2809–2825, 2003) to algebraic-geometric codes.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10623-023-01333-2</doi><tpages>16</tpages><orcidid>https://orcid.org/0000-0001-8924-7605</orcidid><orcidid>https://orcid.org/0000-0003-0977-5999</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0925-1022 |
| ispartof | Designs, codes, and cryptography, 2024-05, Vol.92 (5), p.1127-1142 |
| issn | 0925-1022 1573-7586 |
| language | eng |
| recordid | cdi_proquest_journals_3050231356 |
| source | Springer Nature |
| subjects | BCH codes Coding and Information Theory Computer Science Cryptology Discrete Mathematics in Computer Science Lattices Soft decision decoding |
| title | Construction-D lattice from Garcia–Stichtenoth tower code |
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