Construction of quasi-self-dual codes over a commutative non-unital ring of order 4
- 주제어 (키워드) building-up construction , codes , quasi-self-dual , rings
- 발행기관 서강대학교 일반대학원
- 지도교수 김종락
- 발행년도 2022
- 학위수여년월 2022. 8
- 학위명 박사
- 학과 및 전공 일반대학원 수학과
- 실제 URI http://www.dcollection.net/handler/sogang/000000066861
- UCI I804:11029-000000066861
- 본문언어 영어
- 저작권 서강대학교 논문은 저작권 보호를 받습니다.
초록
I denotes a commutative non-unital ring of order 4 defined by generators and relations. Recently, Alahmadi et al. classified quasi-self-dual (QSD) codes, Type IV codes (QSD codes with even weights) and quasi-Type IV codes (QSD codes with even torsion code) over I up to lengths n = 6, and suggested two building-up methods for constructing QSD codes. In this thesis, we give construction results of more QSD codes, Type IV codes and quasi-Type IV codes for lengths n = 7 and 8, and provide five new variants of the two building-up construction methods. For n = 8, it is found that there is at least one QSD code with minimun distance 4, which achieves the highest minimum distance up to present, and we provide a generator matrix for the code. We also show some QSD codes, Type IV codes and quasi-Type IV codes with new weight distributions.
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