由扭转里德-所罗门码构造的LCP和LCD码
Constructions of LCPs and LCD codes from twisted Reed-Solomon codes
- Central China Normal University（华中师范大学）
- Faculty of Mathematics and Statistics, Hubei University（湖北大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究扭转里德-所罗门码的线性互补对与线性互补对偶码，给出构成LCP的必要与充分条件及显式构造，并得到MDS LCP。
AI中文摘要：
线性互补对（LCP）和线性互补对偶（LCD）码在正交直接和掩蔽（ODSM）中具有重要应用，ODSM为对抗侧信道攻击和故障注入攻击提供了有效的对策。虽然LCD码已被广泛研究，但关于一般LCP的结果相对较少。本文进一步研究了扭转里德-所罗门（TRS）码的LCP。我们推导了两个TRS码构成LCP的必要条件，并建立了若干充分条件和显式构造。我们还研究了由TRS码构造的LCD码，并考察了所得LCP的安全参数。此外，在适当条件下，我们获得了TRS码的MDS LCP。
英文摘要：
Linear complementary pairs (LCPs) and linear complementary dual (LCD) codes have important applications in orthogonal direct-sum masking (ODSM), which provides effective countermeasures against side-channel attacks and fault-injection attacks. While LCD codes have been extensively investigated, comparatively fewer results are available for general LCPs. In this paper, we further investigate LCPs of twisted Reed--Solomon (TRS) codes. We derive necessary conditions for two TRS codes to form an LCP and establish several sufficient conditions and explicit constructions. We also study LCD codes constructed from TRS codes and investigate the security parameters of the resulting LCPs. Furthermore, under suitable conditions, we obtain MDS LCPs of TRS codes.
