Loading…
An application of coding theory to estimating Davenport constants
We investigate a certain well-established generalization of the Davenport constant. For j a positive integer (the case j = 1, is the classical one) and a finite Abelian group ( G , +, 0), the invariant D j ( G ) is defined as the smallest ℓ such that each sequence over G of length at least ℓ has j...
Saved in:
| Published in: | Designs, codes, and cryptography codes, and cryptography, 2011, Vol.61 (1), p.105-118 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| cited_by | cdi_FETCH-LOGICAL-c322t-f20f4ddff7ed27c9209d85644a36abd853869cbfc6e9fc6d40a778a08020fd473 |
|---|---|
| cites | cdi_FETCH-LOGICAL-c322t-f20f4ddff7ed27c9209d85644a36abd853869cbfc6e9fc6d40a778a08020fd473 |
| container_end_page | 118 |
| container_issue | 1 |
| container_start_page | 105 |
| container_title | Designs, codes, and cryptography |
| container_volume | 61 |
| creator | Plagne, Alain Schmid, Wolfgang A. |
| description | We investigate a certain well-established generalization of the Davenport constant. For
j
a positive integer (the case
j
= 1, is the classical one) and a finite Abelian group (
G
, +, 0), the invariant D
j
(
G
) is defined as the smallest
ℓ
such that each sequence over
G
of length at least
ℓ
has
j
disjoint non-empty zero-sum subsequences. We investigate these quantities for elementary 2-groups of large rank (relative to
j
). Using tools from coding theory, we give fairly precise estimates for these quantities. We use our results to give improved bounds for the classical Davenport constant of certain groups. |
| doi_str_mv | 10.1007/s10623-010-9441-5 |
| format | article |
| fullrecord | <record><control><sourceid>hal_cross</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_00851517v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>oai_HAL_hal_00851517v1</sourcerecordid><originalsourceid>FETCH-LOGICAL-c322t-f20f4ddff7ed27c9209d85644a36abd853869cbfc6e9fc6d40a778a08020fd473</originalsourceid><addsrcrecordid>eNp9kE1PwzAMhiMEEmPwA7j1yiHgfDXtsRqwIU3iAucoa5Kt00iqJEzavydTEUcutmW_j2W_CN0TeCQA8ikRqCnDQAC3nBMsLtCMCMmwFE19iWbQUoEJUHqNblLaAwBhQGeo63ylx_Ew9DoPwVfBVX0wg99WeWdDPFU5VDbl4auMS_NZH60fQ8xF5VPWPqdbdOX0Idm73zxHn68vH4sVXr8v3xbdGveM0owdBceNcU5aQ2XfUmhNI2rONav1ppSsqdt-4_ratiUYDlrKRkMDBTRcsjl6mPbu9EGNsVwUTyroQa26tTr3ABpBBJFHUrRk0vYxpBSt-wMIqLNfavJLFb_U2S8lCkMnJhWt39qo9uE7-vLSP9APWehtTA</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>An application of coding theory to estimating Davenport constants</title><source>Springer Link</source><creator>Plagne, Alain ; Schmid, Wolfgang A.</creator><creatorcontrib>Plagne, Alain ; Schmid, Wolfgang A.</creatorcontrib><description>We investigate a certain well-established generalization of the Davenport constant. For
j
a positive integer (the case
j
= 1, is the classical one) and a finite Abelian group (
G
, +, 0), the invariant D
j
(
G
) is defined as the smallest
ℓ
such that each sequence over
G
of length at least
ℓ
has
j
disjoint non-empty zero-sum subsequences. We investigate these quantities for elementary 2-groups of large rank (relative to
j
). Using tools from coding theory, we give fairly precise estimates for these quantities. We use our results to give improved bounds for the classical Davenport constant of certain groups.</description><identifier>ISSN: 0925-1022</identifier><identifier>EISSN: 1573-7586</identifier><identifier>DOI: 10.1007/s10623-010-9441-5</identifier><language>eng</language><publisher>Boston: Springer US</publisher><subject>Circuits ; Coding and Information Theory ; Computer Science ; Cryptology ; Data Structures and Information Theory ; Discrete Mathematics in Computer Science ; Information and Communication ; Mathematics</subject><ispartof>Designs, codes, and cryptography, 2011, Vol.61 (1), p.105-118</ispartof><rights>Springer Science+Business Media, LLC 2010</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c322t-f20f4ddff7ed27c9209d85644a36abd853869cbfc6e9fc6d40a778a08020fd473</citedby><cites>FETCH-LOGICAL-c322t-f20f4ddff7ed27c9209d85644a36abd853869cbfc6e9fc6d40a778a08020fd473</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,27923,27924</link.rule.ids><backlink>$$Uhttps://hal.science/hal-00851517$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Plagne, Alain</creatorcontrib><creatorcontrib>Schmid, Wolfgang A.</creatorcontrib><title>An application of coding theory to estimating Davenport constants</title><title>Designs, codes, and cryptography</title><addtitle>Des. Codes Cryptogr</addtitle><description>We investigate a certain well-established generalization of the Davenport constant. For
j
a positive integer (the case
j
= 1, is the classical one) and a finite Abelian group (
G
, +, 0), the invariant D
j
(
G
) is defined as the smallest
ℓ
such that each sequence over
G
of length at least
ℓ
has
j
disjoint non-empty zero-sum subsequences. We investigate these quantities for elementary 2-groups of large rank (relative to
j
). Using tools from coding theory, we give fairly precise estimates for these quantities. We use our results to give improved bounds for the classical Davenport constant of certain groups.</description><subject>Circuits</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>Mathematics</subject><issn>0925-1022</issn><issn>1573-7586</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9kE1PwzAMhiMEEmPwA7j1yiHgfDXtsRqwIU3iAucoa5Kt00iqJEzavydTEUcutmW_j2W_CN0TeCQA8ikRqCnDQAC3nBMsLtCMCMmwFE19iWbQUoEJUHqNblLaAwBhQGeo63ylx_Ew9DoPwVfBVX0wg99WeWdDPFU5VDbl4auMS_NZH60fQ8xF5VPWPqdbdOX0Idm73zxHn68vH4sVXr8v3xbdGveM0owdBceNcU5aQ2XfUmhNI2rONav1ppSsqdt-4_ratiUYDlrKRkMDBTRcsjl6mPbu9EGNsVwUTyroQa26tTr3ABpBBJFHUrRk0vYxpBSt-wMIqLNfavJLFb_U2S8lCkMnJhWt39qo9uE7-vLSP9APWehtTA</recordid><startdate>2011</startdate><enddate>2011</enddate><creator>Plagne, Alain</creator><creator>Schmid, Wolfgang A.</creator><general>Springer US</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope></search><sort><creationdate>2011</creationdate><title>An application of coding theory to estimating Davenport constants</title><author>Plagne, Alain ; Schmid, Wolfgang A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c322t-f20f4ddff7ed27c9209d85644a36abd853869cbfc6e9fc6d40a778a08020fd473</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Circuits</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>Mathematics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Plagne, Alain</creatorcontrib><creatorcontrib>Schmid, Wolfgang A.</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Designs, codes, and cryptography</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Plagne, Alain</au><au>Schmid, Wolfgang A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An application of coding theory to estimating Davenport constants</atitle><jtitle>Designs, codes, and cryptography</jtitle><stitle>Des. Codes Cryptogr</stitle><date>2011</date><risdate>2011</risdate><volume>61</volume><issue>1</issue><spage>105</spage><epage>118</epage><pages>105-118</pages><issn>0925-1022</issn><eissn>1573-7586</eissn><abstract>We investigate a certain well-established generalization of the Davenport constant. For
j
a positive integer (the case
j
= 1, is the classical one) and a finite Abelian group (
G
, +, 0), the invariant D
j
(
G
) is defined as the smallest
ℓ
such that each sequence over
G
of length at least
ℓ
has
j
disjoint non-empty zero-sum subsequences. We investigate these quantities for elementary 2-groups of large rank (relative to
j
). Using tools from coding theory, we give fairly precise estimates for these quantities. We use our results to give improved bounds for the classical Davenport constant of certain groups.</abstract><cop>Boston</cop><pub>Springer US</pub><doi>10.1007/s10623-010-9441-5</doi><tpages>14</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0925-1022 |
| ispartof | Designs, codes, and cryptography, 2011, Vol.61 (1), p.105-118 |
| issn | 0925-1022 1573-7586 |
| language | eng |
| recordid | cdi_hal_primary_oai_HAL_hal_00851517v1 |
| source | Springer Link |
| subjects | Circuits Coding and Information Theory Computer Science Cryptology Data Structures and Information Theory Discrete Mathematics in Computer Science Information and Communication Mathematics |
| title | An application of coding theory to estimating Davenport constants |
| url | http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-10T10%3A42%3A32IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-hal_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=An%20application%20of%20coding%20theory%20to%20estimating%20Davenport%20constants&rft.jtitle=Designs,%20codes,%20and%20cryptography&rft.au=Plagne,%20Alain&rft.date=2011&rft.volume=61&rft.issue=1&rft.spage=105&rft.epage=118&rft.pages=105-118&rft.issn=0925-1022&rft.eissn=1573-7586&rft_id=info:doi/10.1007/s10623-010-9441-5&rft_dat=%3Chal_cross%3Eoai_HAL_hal_00851517v1%3C/hal_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c322t-f20f4ddff7ed27c9209d85644a36abd853869cbfc6e9fc6d40a778a08020fd473%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |