극소 부호의 새로운 확장 기법
A New Extension Method for Minimal Codes
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
비밀 공유 기법에서는 비밀 정보가 사용자들에게 분산되어 저장되고, 특정 허가된 사용자의 부분 집합으로부터만 비밀이 재합성될 수 있어야 한다. 이를 위해서는 서로 다른 부호어들 사이의 정보가 종속되지 않아야 한다. 극소 부호는 선형 블록 부호의 일종으로서 이러한 비밀 정보들이 상호 종속되지 않게 분산하는 역할을 한다. 본 논문에서는 극소 부호의 새로운 확장 기법을 제시한다. 임의의 벡터와 극소 부호의 곱을 통해 새로운 길이와 해밍 무게를 가지는 새로운 극소 부호가 생성된다. 이를 통해 기존에 알려지지않은 파라미터를 가지는 극소 부호들을 제공할 수 있다.
Abstract
In a secret sharing scheme, secret information must be distributed and stored to users, and confidentiality mustbe able to be reconstructed only from an authorized subset of users. To do this, secret information amongdifferent code words must not be subordinate to each other. The minimal code is a kind of linear block code todistribute these secret information not mutually dependent. In this paper, we present a novel extension techniquefor minimal codes. The product of an arbitrary vector and a minimal code produces a new minimal code with anextended length and Hamming weight. Accordingly, it is possible to provide minimal codes with parameters notknown in the literature.
참고문헌 (11)
- W. E. Ryan, "Channel Codes" (2009), Cambridge University Press
- J. L. Massey, "Minimal codewords and ecret sharing", Proc. 6th Joint Swedish-Russian Int. Workshop Inform. Theory, pp.276~279 (1993)
- A. Ashikhmin, "Minimal vectors in linear codes", IEEE Transactions on Information Theory, 44(5), pp.2010~2017 (1998), Institute of Electrical and Electronics Engineers (IEEE)[DOI]
- C. Carlet, "Linear Codes From Perfect Nonlinear Mappings and Their Secret Sharing Schemes", IEEE Transactions on Information Theory, 51(6), pp.2089~2102 (2005), Institute of Electrical and Electronics Engineers (IEEE)[DOI]
- Jin Yuan, "Secret sharing schemes from three classes of linear codes", IEEE Transactions on Information Theory, 52(1), pp.206~212 (2006), Institute of Electrical and Electronics Engineers (IEEE)[DOI]
- Kelan Ding, "A Class of Two-Weight and Three-Weight Codes and Their Applications in Secret Sharing", IEEE Transactions on Information Theory, 61(11), pp.5835~5842 (2015), Institute of Electrical and Electronics Engineers (IEEE)[DOI]
- Seunghwan Chang, "Linear codes from simplicial complexes", Designs, Codes and Cryptography, 86(10), pp.2167~2181 (2017), Springer Science and Business Media LLC[DOI]
- Cunsheng Ding, "Minimal Binary Linear Codes", IEEE Transactions on Information Theory, 64(10), pp.6536~6545 (2018), Institute of Electrical and Electronics Engineers (IEEE)[DOI]
- Ziling Heng, "Minimal linear codes over finite fields", Finite Fields and Their Applications, 54, pp.176~196 (2018), Elsevier BV[DOI]
- Daniele Bartoli, "Minimal Linear Codes in Odd Characteristic", IEEE Transactions on Information Theory, 65(7), pp.4152~4155 (2019), Institute of Electrical and Electronics Engineers (IEEE)[DOI]
- Sihem Mesnager, "Minimal Linear Codes From Characteristic Functions", IEEE Transactions on Information Theory, 66(9), pp.5404~5413 (2020), Institute of Electrical and Electronics Engineers (IEEE)[DOI]