A lower bound on permutation codes of distance n-1
A classical recursive construction for mutually orthogonal latin squares (MOLS) is shown to hold more generally for a class of permutation codes of length n and minimum distance n - 1 . When such codes of length p + 1 are included as ingredients, we obtain a general lower bound M ( n , n - 1 ) ≥ n 1...
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| Veröffentlicht in: | Designs, codes, and cryptography codes, and cryptography, 2020, Vol.88 (1), p.63-72 |
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| container_title | Designs, codes, and cryptography |
| container_volume | 88 |
| creator | Bereg, Sergey Dukes, Peter J. |
| description | A classical recursive construction for mutually orthogonal latin squares (MOLS) is shown to hold more generally for a class of permutation codes of length
n
and minimum distance
n
-
1
. When such codes of length
p
+
1
are included as ingredients, we obtain a general lower bound
M
(
n
,
n
-
1
)
≥
n
1.0797
for large
n
, gaining a small improvement on the guarantee given from MOLS. |
| doi_str_mv | 10.1007/s10623-019-00670-5 |
| format | Article |
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n
and minimum distance
n
-
1
. When such codes of length
p
+
1
are included as ingredients, we obtain a general lower bound
M
(
n
,
n
-
1
)
≥
n
1.0797
for large
n
, gaining a small improvement on the guarantee given from MOLS.</description><identifier>ISSN: 0925-1022</identifier><identifier>EISSN: 1573-7586</identifier><identifier>DOI: 10.1007/s10623-019-00670-5</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Arrays ; Circuits ; Codes ; Coding and Information Theory ; Computer Science ; Cryptology ; Data Structures and Information Theory ; Discrete Mathematics in Computer Science ; Information and Communication ; Latin square design ; Lower bounds ; Permutations</subject><ispartof>Designs, codes, and cryptography, 2020, Vol.88 (1), p.63-72</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2019</rights><rights>Copyright Springer Nature B.V. 2020</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-1622902188395340f7db528a4a3ca88898bc92a20482302e6593a9bb93e61a0f3</citedby><cites>FETCH-LOGICAL-c319t-1622902188395340f7db528a4a3ca88898bc92a20482302e6593a9bb93e61a0f3</cites><orcidid>0000-0002-2866-6766</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10623-019-00670-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10623-019-00670-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27922,27923,41486,42555,51317</link.rule.ids></links><search><creatorcontrib>Bereg, Sergey</creatorcontrib><creatorcontrib>Dukes, Peter J.</creatorcontrib><title>A lower bound on permutation codes of distance n-1</title><title>Designs, codes, and cryptography</title><addtitle>Des. Codes Cryptogr</addtitle><description>A classical recursive construction for mutually orthogonal latin squares (MOLS) is shown to hold more generally for a class of permutation codes of length
n
and minimum distance
n
-
1
. When such codes of length
p
+
1
are included as ingredients, we obtain a general lower bound
M
(
n
,
n
-
1
)
≥
n
1.0797
for large
n
, gaining a small improvement on the guarantee given from MOLS.</description><subject>Arrays</subject><subject>Circuits</subject><subject>Codes</subject><subject>Coding and Information Theory</subject><subject>Computer Science</subject><subject>Cryptology</subject><subject>Data Structures and Information Theory</subject><subject>Discrete Mathematics in Computer Science</subject><subject>Information and Communication</subject><subject>Latin square design</subject><subject>Lower bounds</subject><subject>Permutations</subject><issn>0925-1022</issn><issn>1573-7586</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhoMouK7-AU8Bz9HJTJMmx0X8ggUveg5pm8ouu82atIj_3mgFb55mDu_zzvAwdinhWgLUN1mCRhIgrQDQNQh1xBZS1SRqZfQxW4BFJSQgnrKznLcAIAlwwXDFd_EjJN7Eaeh4HPghpP00-nFT9jZ2IfPY826TRz-0gQ9CnrOT3u9yuPidS_Z6f_dy-yjWzw9Pt6u1aEnaUUiNaAGlMWQVVdDXXaPQ-MpT640x1jStRY9QGSyvBK0seds0loKWHnpasqu595Di-xTy6LZxSkM56ZCIKqmN0SWFc6pNMecUendIm71Pn06C-3bjZjeuuHE_bpwqEM1QLuHhLaS_6n-oL-UfY3k</recordid><startdate>2020</startdate><enddate>2020</enddate><creator>Bereg, Sergey</creator><creator>Dukes, Peter J.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-2866-6766</orcidid></search><sort><creationdate>2020</creationdate><title>A lower bound on permutation codes of distance n-1</title><author>Bereg, Sergey ; Dukes, Peter J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-1622902188395340f7db528a4a3ca88898bc92a20482302e6593a9bb93e61a0f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Arrays</topic><topic>Circuits</topic><topic>Codes</topic><topic>Coding and Information Theory</topic><topic>Computer Science</topic><topic>Cryptology</topic><topic>Data Structures and Information Theory</topic><topic>Discrete Mathematics in Computer Science</topic><topic>Information and Communication</topic><topic>Latin square design</topic><topic>Lower bounds</topic><topic>Permutations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bereg, Sergey</creatorcontrib><creatorcontrib>Dukes, Peter J.</creatorcontrib><collection>CrossRef</collection><jtitle>Designs, codes, and cryptography</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bereg, Sergey</au><au>Dukes, Peter J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A lower bound on permutation codes of distance n-1</atitle><jtitle>Designs, codes, and cryptography</jtitle><stitle>Des. Codes Cryptogr</stitle><date>2020</date><risdate>2020</risdate><volume>88</volume><issue>1</issue><spage>63</spage><epage>72</epage><pages>63-72</pages><issn>0925-1022</issn><eissn>1573-7586</eissn><abstract>A classical recursive construction for mutually orthogonal latin squares (MOLS) is shown to hold more generally for a class of permutation codes of length
n
and minimum distance
n
-
1
. When such codes of length
p
+
1
are included as ingredients, we obtain a general lower bound
M
(
n
,
n
-
1
)
≥
n
1.0797
for large
n
, gaining a small improvement on the guarantee given from MOLS.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10623-019-00670-5</doi><tpages>10</tpages><orcidid>https://orcid.org/0000-0002-2866-6766</orcidid></addata></record> |
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| ispartof | Designs, codes, and cryptography, 2020, Vol.88 (1), p.63-72 |
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| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Arrays Circuits Codes Coding and Information Theory Computer Science Cryptology Data Structures and Information Theory Discrete Mathematics in Computer Science Information and Communication Latin square design Lower bounds Permutations |
| title | A lower bound on permutation codes of distance n-1 |
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