Relative generalized Hamming weights of cyclic codes
Relative generalized Hamming weights of cyclic codes
复制标题
循环码的相对广义汉明权
DOI：
10.1016/j.ffa.2017.12.008
复制
发表时间：
2018
影响因子：
1
通讯作者：
Feng Keqin
中科院分区：
文献类型：
--
作者：
Zhang Jun;Feng Keqin
线性码相对于线性子码的相对广义汉明权重决定了基于线性码的线性斜坡秘密共享方案的安全性。它们可以用来表示当某些股份的保管人腐败时，秘密信息的泄露。循环码是一种有趣的线性码，在通信和存储系统中有着广泛的应用。本文研究了两个非零循环码相对于其不可约循环子码的rghw。我们给出了循环码的rghw的两个公式。作为公式的应用，计算了显式算例。此外，与rghw的广义Plotkin界相比，算例中循环码的rghw非常大。这为基于双码的秘密共享方案提供了很高的安全性。
Relative generalized Hamming weights (RGHWs) of a linear code with respect to a linear subcode determine the security of the linear ramp secret sharing scheme based on the linear codes. They can be used to express the information leakage of the secret when some keepers of shares are corrupted. Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems. In this paper, we investigate the RGHWs of cyclic codes of two nonzeros with respect to its irreducible cyclic subcodes. We give two formulae for RGHWs of the cyclic codes. As applications of the formulae, explicit examples are computed. Moreover, RGHWs of cyclic codes in the examples are very large, comparing with the generalized Plotkin bound of RGHWs. So it guarantees very high security for the secret sharing scheme based on the dual codes.