Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 이윤진 | - |
dc.contributor.author | 김지애 | - |
dc.creator | 김지애 | - |
dc.date.accessioned | 2016-08-25T10:08:07Z | - |
dc.date.available | 2016-08-25T10:08:07Z | - |
dc.date.issued | 2010 | - |
dc.identifier.other | OAK-000000056924 | - |
dc.identifier.uri | https://dspace.ewha.ac.kr/handle/2015.oak/185345 | - |
dc.identifier.uri | http://dcollection.ewha.ac.kr/jsp/common/DcLoOrgPer.jsp?sItemId=000000056924 | - |
dc.description.abstract | In this thesis, we study construction method of self-dual codes over GF(p^(k)) or Z_(pk) using Diophantine equations. We also show that self-dual codes con-structed by one-block construction, two-block construction and four-block con-struction with m=2 are also quasi-cyclic. We construct various examples of self-dual codes over non-prime nite elds GF(p^(k)) for p^(k) = 3², 3³, 3⁴, 3^(5), 3^(6), 3^(8), 3^(10), 5², 5³, 5₄, 5^(6), 7², 7³, 7⁴, 11², 11³, and nite rings Zpk for pk = 3³, 3⁴, 5², 5³, 5⁴, 7², 7³, 11², 11³, 13², 13², 13³, 17², 17³, 29², 29³.;이 논문에서는 유한 체 GF(p^(k))와 유한 환 Z_(pk)위에서 디오판토스의 방정식을 사용한 self-dual code를 만드는 방법에 대해서 공부한다. 또한 one-block construction, two-block construction 그리고 m=2 일 때의 four-block construction은 quasi-cyclic code가 됨을 보인다. 마지막으로 유한 체와 유한 환 위에서 다양한 self-dual code의 예제들을 기재했다. | - |
dc.description.tableofcontents | I. Introduction = 1 II. Preliminaries = 4 III. Self-dual Codes over GF(p) and Examples = 6 IV. Self-dual Codes over GF(pk) and Examples = 13 V. Self-dual Codes over Zpk and Examples = 27 VI. Connection with Quasi-cyclic Codes = 33 References = 42 국문초록 = 45 | - |
dc.format | application/pdf | - |
dc.format.extent | 592141 bytes | - |
dc.language | eng | - |
dc.publisher | 이화여자대학교 대학원 | - |
dc.title | Self-dual Code Construction over GF(p^k) and Z_p^k via Diophantine Equations | - |
dc.type | Master's Thesis | - |
dc.format.page | ⅱ, 45 p. | - |
dc.identifier.thesisdegree | Master | - |
dc.identifier.major | 대학원 수학과 | - |
dc.date.awarded | 2010. 2 | - |