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초록
We examine the main linear coding theory problem and study the structure of optimal linear codes over the ring ℤ<inf>m</inf>. We derive bounds on the maximum Hamming weight of these codes. We give bounds on the best linear codes over ℤ<inf>8</inf> and ℤ<inf>9</inf> of lengths up to 6. We determine the minimum distances of optimal linear codes over ℤ<inf>4</inf> for lengths up to 7. Some examples of optimal codes are given. © 2007 The Korean Mathematical Society.
키워드
Codes over rings; Linear codes; Optimal codes
- 제목
- Optimal linear codes over ℤm
- 저자
- Dougherty, Steven T.; Gulliver, Thomas Aaron; Park, Young Ho O.; Wong, John N.C.
- 발행일
- 2007
- 유형
- Article
- 저널명
- 대한수학회지
- 권
- 44
- 호
- 5
- 페이지
- 1139 ~ 1162