New Parameters of Linear Codes Expressing Security Performance of Universal Secure Network Coding
The universal secure network coding presented by Silva et al. realizes secure and reliable transmission of a secret message over any underlying network code, by using maximum rank distance codes. Inspired by their result, this paper considers the secure network coding based on arbitrary linear codes, and investigates its security performance and error correction capability that are guaranteed independently of the underlying network code. The security performance and error correction capability are said to be universal when they are independent of underlying network codes. This paper introduces new code parameters, the Relative Dimension/Intersection Profile (RDIP) and the Relative Generalized Rank Weight (RGRW) of linear codes.