Browse > Article
http://dx.doi.org/10.7471/ikeee.2022.26.3.506

A New Extension Method for Minimal Codes  

Chung, Jin-Ho (Dept. of Electrical, Electronics, and Computer Engineering, University of Ulsan)
Publication Information
Journal of IKEEE / v.26, no.3, 2022 , pp. 506-509 More about this Journal
Abstract
In a secret sharing scheme, secret information must be distributed and stored to users, and confidentiality must be able to be reconstructed only from an authorized subset of users. To do this, secret information among different code words must not be subordinate to each other. The minimal code is a kind of linear block code to distribute these secret information not mutually dependent. In this paper, we present a novel extension technique for minimal codes. The product of an arbitrary vector and a minimal code produces a new minimal code with an extended length and Hamming weight. Accordingly, it is possible to provide minimal codes with parameters not known in the literature.
Keywords
Finite fields; interleaving; linear codes; minimal codes; secret sharing;
Citations & Related Records
연도 인용수 순위
  • Reference
1 D. Bartoli and M. Bonini, "Minimal linear codes in odd characteristic," IEEE Trans. Inf. Theory, vol.65, no.7, pp.4152-4155, 2019. DOI: 10.1109/TIT.2019.2891992   DOI
2 S. Mesnager, Y. Qi, H. Ru, and C. Tang, "Minimal linear codes from characteristic functions," IEEE Trans. Inf. Theory, vol.66, no.9, pp.5404-5413, 2020. DOI: 10.1109/TIT.2020.2978387   DOI
3 J. L. Massey, "Minimal codewords and ecret sharing," Proc. 6th Joint Swedish-Russian Int. Workshop Inform. Theory, pp.276-279, 1993.
4 A. Ashikhmin and A. Barg, "Minimal vectors in linear codes," IEEE Trans. Inf. Theory, vol.44, no.5, pp.2010-2017, 1998. DOI: 10.1109/18.705584   DOI
5 J. Yuan and C. Ding, "Secret sharing schemes from three classes of linear codes," IEEE Trans. Inf. Theory, vol.52, no.1, pp.206-212, 2006. DOI: 10.1109/TIT.2005.860412   DOI
6 C. Carlet, C. Ding, and J. Yuan, "Linear codes from perfect nonlinear mappings and their secret sharing schemes," IEEE Trans. Inf. Theory, vol.51, no.6, pp.2089-2102, 2005. DOI: 10.1109/TIT.2005.847722   DOI
7 K. Ding and C. Ding, "A class of two-weight and three-weight codes and their applications in secret sharing," IEEE Trans. Inf. Theory, vol.61, no.11, pp.5835-5842, 2015. DOI: 10.1109/TIT.2015.2473861   DOI
8 C. Ding, Z. Heng, and Z. Zhou, "Minimal binary linear codes," IEEE Trans. Inf. Theory, vol.64, no.10, pp.6536-6545, 2018. DOI: 10.1109/TIT.2018.2819196   DOI
9 Z. Heng, C. Ding, and Z. Zhou, "Minimal linear codes over finite fields," Finite Fields Their Appl., vol.54, pp.176-196, 2018. DOI: 10.1016/j.ffa.2018.08.010   DOI
10 W. E. Ryan, S. Lin, Channel Codes, 2nd ed.; Cambridge University Press, UK, 2009.
11 S. Chang and J. Y. Hyun, "Linear codes from simplicial complexes," Des., Codes Cryptogr., vol.86, no.10, pp.2167-2181, 2018. DOI: 10.1007/s10623-017-0442-5   DOI