Full metadata record
DC Field | Value | Language |
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dc.contributor.author | 이윤진 | * |
dc.date.accessioned | 2018-12-14T16:31:10Z | - |
dc.date.available | 2018-12-14T16:31:10Z | - |
dc.date.issued | 2018 | * |
dc.identifier.issn | 1071-5797 | * |
dc.identifier.other | OAK-22460 | * |
dc.identifier.uri | https://dspace.ewha.ac.kr/handle/2015.oak/247833 | - |
dc.description.abstract | We study self-dual codes over a factor ring R=Fq[X]/(Xm−1) of length ℓ, equivalently, ℓ-quasi-cyclic self-dual codes of length mℓ over a finite field Fq, provided that the polynomial Xm−1 has exactly three distinct irreducible factors in Fq[X], where Fq is the finite field of order q. There are two types of the ring R depending on how the conjugation map acts on the minimal ideals of R. We show that every self-dual code over the ring R of the first type with length ≥6 has free rank ≥2. This implies that every ℓ-quasi-cyclic self-dual code of length mℓ≥6m over Fq can be obtained by the building-up construction, where m corresponds to the ring R of the first type. On the other hand, there exists a self-dual code of free rank ≤1 over the ring R of the second type. We explicitly determine the forms of generator matrices of all self-dual codes over R of free rank ≤1. For the case that m=7, we find 9828 binary 10-quasi-cyclic self-dual codes of length 70 with minimum weight 12, up to equivalence, which are constructed from self-dual codes over the ring R of the second type. These codes are all new codes. Furthermore, for the case that m=17, we find 1566 binary 4-quasi-cyclic self-dual codes of length 68 with minimum weight 12, up to equivalence, which are constructed from self-dual codes over the ring R of the first type. © 2018 Elsevier Inc. | * |
dc.language | English | * |
dc.publisher | Academic Press Inc. | * |
dc.subject | Extremal code | * |
dc.subject | Finite field | * |
dc.subject | Quasi-cyclic code | * |
dc.subject | Self-dual code | * |
dc.title | Extremal quasi-cyclic self-dual codes over finite fields | * |
dc.type | Article | * |
dc.relation.volume | 52 | * |
dc.relation.index | SCIE | * |
dc.relation.index | SCOPUS | * |
dc.relation.startpage | 301 | * |
dc.relation.lastpage | 318 | * |
dc.relation.journaltitle | Finite Fields and their Applications | * |
dc.identifier.doi | 10.1016/j.ffa.2018.04.013 | * |
dc.identifier.wosid | WOS:000435229400018 | * |
dc.identifier.scopusid | 2-s2.0-85046665416 | * |
dc.author.google | Kim H.J. | * |
dc.author.google | Lee Y. | * |
dc.contributor.scopusid | 이윤진(23100337700) | * |
dc.date.modifydate | 20240123113558 | * |