컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0301 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Combinatorics / Graph Theory / Cryptography / Coding Theory (SS-05) |
| 영문제목 (Title(Eng.)) |
On Euclidean self-dual extended split group codes |
| 저자(Author(s)) |
Lilibeth Dicuangco Valdez1, Aldrin Ocampo1 Institute of Mathematics, University of the Philippines, Diliman, QuezonCity1 |
| 초록본문(Abstract) | Split group codes are a generalization of an important class of cyclic codes called duadic codes. In this paper, we characterize all Euclidean self-orthogonal group codes in $F\left[G^{*}\right]$, where $F$ is a finite field and $G^{*}$ is the dual of a finite abelian group $G$. We also show that group codes in $F\left[G^{*}\right]$, where $F=\mathbb{F}_{q^{2}}$, whose extension by a suitable parity-check coordinate are self-dual, are precisely the split group codes in $F\left[G^{*}\right]$ for some splitting of $G$ over $Z=\left\{ 0\right\} $ by $-1$. Moreover, we show that such extended group codes exist if $ord_{r}\left(q\right)\equiv2\left(mod4\right)$ for every divisor $r$ of the exponent of $G$. |
| 분류기호 (MSC number(s)) |
11T71 |
| 키워드(Keyword(s)) | split group codes, splitting, self-orthogonal, extended codes |
| 강연 형태 (Language of Session (Talk)) |
English |