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Complete weight enumerators of some linear codes from quadratic forms
Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a construction of q -ary linear codes with few weights employing general quadratic forms over the finite field F q is proposed, where q is an odd...
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| Published in: | Cryptography and communications 2017-01, Vol.9 (1), p.151-163 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c382t-14d6cf189c5a4588dfa731e6b71f3d69992725769fc49868daf258ca06eb6a8a3 |
| container_end_page | 163 |
| container_issue | 1 |
| container_start_page | 151 |
| container_title | Cryptography and communications |
| container_volume | 9 |
| creator | Zhang, Dan Fan, Cuiling Peng, Daiyuan Tang, Xiaohu |
| description | Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a construction of
q
-ary linear codes with few weights employing general quadratic forms over the finite field
F
q
is proposed, where
q
is an odd prime power. This generalizes some earlier constructions of
p
-ary linear codes from quadratic bent functions over the prime field
F
p
, where
p
is an odd prime. The complete weight enumerators of the resultant
q
-ary linear codes are also determined. |
| doi_str_mv | 10.1007/s12095-016-0190-9 |
| format | article |
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q
-ary linear codes with few weights employing general quadratic forms over the finite field
F
q
is proposed, where
q
is an odd prime power. This generalizes some earlier constructions of
p
-ary linear codes from quadratic bent functions over the prime field
F
p
, where
p
is an odd prime. The complete weight enumerators of the resultant
q
-ary linear codes are also determined.</description><identifier>ISSN: 1936-2447</identifier><identifier>EISSN: 1936-2455</identifier><identifier>DOI: 10.1007/s12095-016-0190-9</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Binary system ; Circuits ; Codes ; Coding and Information Theory ; Communications Engineering ; Computer Science ; Data Structures and Information Theory ; Information and Communication ; Linear codes ; Mathematics of Computing ; Networks ; Quadratic forms</subject><ispartof>Cryptography and communications, 2017-01, Vol.9 (1), p.151-163</ispartof><rights>Springer Science+Business Media New York 2016</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c382t-14d6cf189c5a4588dfa731e6b71f3d69992725769fc49868daf258ca06eb6a8a3</citedby><cites>FETCH-LOGICAL-c382t-14d6cf189c5a4588dfa731e6b71f3d69992725769fc49868daf258ca06eb6a8a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>Zhang, Dan</creatorcontrib><creatorcontrib>Fan, Cuiling</creatorcontrib><creatorcontrib>Peng, Daiyuan</creatorcontrib><creatorcontrib>Tang, Xiaohu</creatorcontrib><title>Complete weight enumerators of some linear codes from quadratic forms</title><title>Cryptography and communications</title><addtitle>Cryptogr. Commun</addtitle><description>Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a construction of
q
-ary linear codes with few weights employing general quadratic forms over the finite field
F
q
is proposed, where
q
is an odd prime power. This generalizes some earlier constructions of
p
-ary linear codes from quadratic bent functions over the prime field
F
p
, where
p
is an odd prime. The complete weight enumerators of the resultant
q
-ary linear codes are also determined.</description><subject>Binary system</subject><subject>Circuits</subject><subject>Codes</subject><subject>Coding and Information Theory</subject><subject>Communications Engineering</subject><subject>Computer Science</subject><subject>Data Structures and Information Theory</subject><subject>Information and Communication</subject><subject>Linear codes</subject><subject>Mathematics of Computing</subject><subject>Networks</subject><subject>Quadratic forms</subject><issn>1936-2447</issn><issn>1936-2455</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kMFKxDAQhoMouK4-gLeA52qSNmlylLK6woIXPYdsOlm7tE03aRHf3pSKePEwzBy-_x_4ELql5J4SUj5EyojiGaEijSKZOkMrqnKRsYLz89-7KC_RVYxHQgRnRb5Cm8p3Qwsj4E9oDh8jhn7qIJjRh4i9w9F3gNumBxOw9TVE7ILv8GkydYIai50PXbxGF860EW5-9hq9P23eqm22e31-qR53mc0lGzNa1MI6KpXlpuBS1s6UOQWxL6nLa6GUYiXjpVDOFkoKWRvHuLSGCNgLI02-RndL7xD8aYI46qOfQp9eaiolkSSVqkTRhbLBxxjA6SE0nQlfmhI929KLLZ1s6dmWnjNsycTE9gcIf5r_DX0Dmz1snw</recordid><startdate>20170101</startdate><enddate>20170101</enddate><creator>Zhang, Dan</creator><creator>Fan, Cuiling</creator><creator>Peng, Daiyuan</creator><creator>Tang, Xiaohu</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20170101</creationdate><title>Complete weight enumerators of some linear codes from quadratic forms</title><author>Zhang, Dan ; Fan, Cuiling ; Peng, Daiyuan ; Tang, Xiaohu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c382t-14d6cf189c5a4588dfa731e6b71f3d69992725769fc49868daf258ca06eb6a8a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Binary system</topic><topic>Circuits</topic><topic>Codes</topic><topic>Coding and Information Theory</topic><topic>Communications Engineering</topic><topic>Computer Science</topic><topic>Data Structures and Information Theory</topic><topic>Information and Communication</topic><topic>Linear codes</topic><topic>Mathematics of Computing</topic><topic>Networks</topic><topic>Quadratic forms</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhang, Dan</creatorcontrib><creatorcontrib>Fan, Cuiling</creatorcontrib><creatorcontrib>Peng, Daiyuan</creatorcontrib><creatorcontrib>Tang, Xiaohu</creatorcontrib><collection>CrossRef</collection><jtitle>Cryptography and communications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhang, Dan</au><au>Fan, Cuiling</au><au>Peng, Daiyuan</au><au>Tang, Xiaohu</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Complete weight enumerators of some linear codes from quadratic forms</atitle><jtitle>Cryptography and communications</jtitle><stitle>Cryptogr. Commun</stitle><date>2017-01-01</date><risdate>2017</risdate><volume>9</volume><issue>1</issue><spage>151</spage><epage>163</epage><pages>151-163</pages><issn>1936-2447</issn><eissn>1936-2455</eissn><abstract>Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a construction of
q
-ary linear codes with few weights employing general quadratic forms over the finite field
F
q
is proposed, where
q
is an odd prime power. This generalizes some earlier constructions of
p
-ary linear codes from quadratic bent functions over the prime field
F
p
, where
p
is an odd prime. The complete weight enumerators of the resultant
q
-ary linear codes are also determined.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s12095-016-0190-9</doi><tpages>13</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1936-2447 |
| ispartof | Cryptography and communications, 2017-01, Vol.9 (1), p.151-163 |
| issn | 1936-2447 1936-2455 |
| language | eng |
| recordid | cdi_proquest_journals_1880805889 |
| source | Springer Nature |
| subjects | Binary system Circuits Codes Coding and Information Theory Communications Engineering Computer Science Data Structures and Information Theory Information and Communication Linear codes Mathematics of Computing Networks Quadratic forms |
| title | Complete weight enumerators of some linear codes from quadratic forms |
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