컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0462 |
|---|---|
| 분류(Section) | Invited Talk |
| 분과(Session) | Combinatorics / Graph Theory / Cryptography / Coding Theory (SS-05) |
| 영문제목 (Title(Eng.)) |
Abelian codes and quasi-abelian codes |
| 저자(Author(s)) |
San Ling1 Division of Mathematical Sciences, School of Physical & Mathematical Sciences, Nanyang Technological University, Singapore 1 |
| 초록본문(Abstract) | Cyclic codes and quasi-cyclic codes over finite fields are important classical block codes that enjoy beautiful algebraic structures and that have found practical applications. They can be naturally viewed, respectively, as ideals in some group algebra ${\mathbb F}[{\mathbb Z}_m]$ or as ${\mathbb F}[{\mathbb Z}_m]$-submodules of $({\mathbb F}[{\mathbb Z}_m])^\ell$, where ${\mathbb F}$ is a finite field and ${\mathbb Z}_m$ is the cyclic group of order $m$. Abelian codes and quasi-abelian codes are natural algebraic generalizations of cyclic codes and quasi-cyclic codes. They are defined to be, respectively, ideals in some group algebra ${\mathbb F}[G]$ and ${\mathbb F}[H]$-submodules of ${\mathbb F}[G]$, where ${\mathbb F}$ is a finite field and $H \le G$ are finite abelian groups. We discuss some properties of these codes as well as certain interesting examples. |
| 분류기호 (MSC number(s)) |
94B05, 94B60 |
| 키워드(Keyword(s)) | abelian codes, quasi-abelian codes, discrete Fourier transform, decomposition, self-dual, self-orthogonal, asymptotic behavior |
| 강연 형태 (Language of Session (Talk)) |
English |