Cyclotomic construction of strong external difference families in finite fields
Strong external difference families (SEDFs) and their generalizations GSEDFs and BGSEDFs in a finite abelian group G are combinatorial designs introduced by Paterson and Stinson (Discret Math 339: 2891–2906, 2016 ) and have applications in communication theory to construct optimal strong algebraic m...
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| Veröffentlicht in: | Designs, codes, and cryptography codes, and cryptography, 2018-05, Vol.86 (5), p.1149-1159 |
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| container_title | Designs, codes, and cryptography |
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| creator | Wen, Jiejing Yang, Minghui Fu, Fangwei Feng, Keqin |
| description | Strong external difference families (SEDFs) and their generalizations GSEDFs and BGSEDFs in a finite abelian group
G
are combinatorial designs introduced by Paterson and Stinson (Discret Math 339: 2891–2906,
2016
) and have applications in communication theory to construct optimal strong algebraic manipulation detection codes. In this paper we firstly present some general constructions of these combinatorial designs by using difference sets and partial difference sets in
G
. Then, as applications of the general constructions, we construct series of SEDF, GSEDF and BGSEDF in finite fields by using cyclotomic classes. Particularly, we present an
(
n
,
m
,
k
,
λ
)
=
(
243
,
11
,
22
,
20
)
-SEDF in
(
F
q
,
+
)
(
q
=
3
5
=
243
)
by using the cyclotomic classes of order 11 in
F
q
which answers an open problem raised in Paterson and Stinson (
2016
). |
| doi_str_mv | 10.1007/s10623-017-0384-y |
| format | Article |
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G
are combinatorial designs introduced by Paterson and Stinson (Discret Math 339: 2891–2906,
2016
) and have applications in communication theory to construct optimal strong algebraic manipulation detection codes. In this paper we firstly present some general constructions of these combinatorial designs by using difference sets and partial difference sets in
G
. Then, as applications of the general constructions, we construct series of SEDF, GSEDF and BGSEDF in finite fields by using cyclotomic classes. Particularly, we present an
(
n
,
m
,
k
,
λ
)
=
(
243
,
11
,
22
,
20
)
-SEDF in
(
F
q
,
+
)
(
q
=
3
5
=
243
)
by using the cyclotomic classes of order 11 in
F
q
which answers an open problem raised in Paterson and Stinson (
2016
).</description><identifier>ISSN: 0925-1022</identifier><identifier>EISSN: 1573-7586</identifier><identifier>DOI: 10.1007/s10623-017-0384-y</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Circuits ; Codes ; Coding and Information Theory ; Combinatorial analysis ; Communication theory ; Computer Science ; Cryptology ; Data Structures and Information Theory ; Discrete Mathematics in Computer Science ; Information and Communication</subject><ispartof>Designs, codes, and cryptography, 2018-05, Vol.86 (5), p.1149-1159</ispartof><rights>Springer Science+Business Media, LLC 2017</rights><rights>Copyright Springer Science & Business Media 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c382t-1dc9c133a50404e56ca0dac27e29ed63334484188d52957d401d44d617d5481e3</citedby><cites>FETCH-LOGICAL-c382t-1dc9c133a50404e56ca0dac27e29ed63334484188d52957d401d44d617d5481e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10623-017-0384-y$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10623-017-0384-y$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Wen, Jiejing</creatorcontrib><creatorcontrib>Yang, Minghui</creatorcontrib><creatorcontrib>Fu, Fangwei</creatorcontrib><creatorcontrib>Feng, Keqin</creatorcontrib><title>Cyclotomic construction of strong external difference families in finite fields</title><title>Designs, codes, and cryptography</title><addtitle>Des. Codes Cryptogr</addtitle><description>Strong external difference families (SEDFs) and their generalizations GSEDFs and BGSEDFs in a finite abelian group
G
are combinatorial designs introduced by Paterson and Stinson (Discret Math 339: 2891–2906,
2016
) and have applications in communication theory to construct optimal strong algebraic manipulation detection codes. In this paper we firstly present some general constructions of these combinatorial designs by using difference sets and partial difference sets in
G
. Then, as applications of the general constructions, we construct series of SEDF, GSEDF and BGSEDF in finite fields by using cyclotomic classes. Particularly, we present an
(
n
,
m
,
k
,
λ
)
=
(
243
,
11
,
22
,
20
)
-SEDF in
(
F
q
,
+
)
(
q
=
3
5
=
243
)
by using the cyclotomic classes of order 11 in
F
q
which answers an open problem raised in Paterson and Stinson (
2016
).</description><subject>Circuits</subject><subject>Codes</subject><subject>Coding and Information Theory</subject><subject>Combinatorial analysis</subject><subject>Communication 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><issn>0925-1022</issn><issn>1573-7586</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LAzEQhoMoWKs_wFvAc3QmH_txlOIXFHrRc1iS2ZKyTTTZgvvv3VLBk6dhhvcZZh7GbhHuEaB-KAiVVAKwFqAaLaYztkBTK1GbpjpnC2ilEQhSXrKrUnYAgArkgm1WkxvSmPbBcZdiGfPBjSFFnno-NyluOX2PlGM3cB_6njJFR7zv9mEIVHiIvA8xjPMo0ODLNbvou6HQzW9dso_np_fVq1hvXt5Wj2vhVCNHgd61DpXqDGjQZCrXge-crEm25CullNaNxqbxRram9hrQa-0rrL3RDZJasrvT3s-cvg5URrtLh-OVxcpZQqVBzd8vGZ5SLqdSMvX2M4d9lyeLYI_e7MmbnRF79GanmZEnpszZuKX8t_l_6Af3zHBk</recordid><startdate>20180501</startdate><enddate>20180501</enddate><creator>Wen, Jiejing</creator><creator>Yang, Minghui</creator><creator>Fu, Fangwei</creator><creator>Feng, Keqin</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20180501</creationdate><title>Cyclotomic construction of strong external difference families in finite fields</title><author>Wen, Jiejing ; Yang, Minghui ; Fu, Fangwei ; Feng, Keqin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c382t-1dc9c133a50404e56ca0dac27e29ed63334484188d52957d401d44d617d5481e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Circuits</topic><topic>Codes</topic><topic>Coding and Information Theory</topic><topic>Combinatorial analysis</topic><topic>Communication 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><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wen, Jiejing</creatorcontrib><creatorcontrib>Yang, Minghui</creatorcontrib><creatorcontrib>Fu, Fangwei</creatorcontrib><creatorcontrib>Feng, Keqin</creatorcontrib><collection>CrossRef</collection><jtitle>Designs, codes, and cryptography</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wen, Jiejing</au><au>Yang, Minghui</au><au>Fu, Fangwei</au><au>Feng, Keqin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Cyclotomic construction of strong external difference families in finite fields</atitle><jtitle>Designs, codes, and cryptography</jtitle><stitle>Des. Codes Cryptogr</stitle><date>2018-05-01</date><risdate>2018</risdate><volume>86</volume><issue>5</issue><spage>1149</spage><epage>1159</epage><pages>1149-1159</pages><issn>0925-1022</issn><eissn>1573-7586</eissn><abstract>Strong external difference families (SEDFs) and their generalizations GSEDFs and BGSEDFs in a finite abelian group
G
are combinatorial designs introduced by Paterson and Stinson (Discret Math 339: 2891–2906,
2016
) and have applications in communication theory to construct optimal strong algebraic manipulation detection codes. In this paper we firstly present some general constructions of these combinatorial designs by using difference sets and partial difference sets in
G
. Then, as applications of the general constructions, we construct series of SEDF, GSEDF and BGSEDF in finite fields by using cyclotomic classes. Particularly, we present an
(
n
,
m
,
k
,
λ
)
=
(
243
,
11
,
22
,
20
)
-SEDF in
(
F
q
,
+
)
(
q
=
3
5
=
243
)
by using the cyclotomic classes of order 11 in
F
q
which answers an open problem raised in Paterson and Stinson (
2016
).</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10623-017-0384-y</doi><tpages>11</tpages></addata></record> |
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| ispartof | Designs, codes, and cryptography, 2018-05, Vol.86 (5), p.1149-1159 |
| issn | 0925-1022 1573-7586 |
| language | eng |
| recordid | cdi_proquest_journals_2017640357 |
| source | SpringerLink Journals |
| subjects | Circuits Codes Coding and Information Theory Combinatorial analysis Communication theory Computer Science Cryptology Data Structures and Information Theory Discrete Mathematics in Computer Science Information and Communication |
| title | Cyclotomic construction of strong external difference families in finite fields |
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