Abstract:
The relative generalized Hamming weight (RGHW) Mr(C,C1) of an [n, k] (linear) code C and an [n, k1] subcode C1, a generalization of generalized Hamming weight (GHW), has ...Show MoreMetadata
Abstract:
The relative generalized Hamming weight (RGHW) Mr(C,C1) of an [n, k] (linear) code C and an [n, k1] subcode C1, a generalization of generalized Hamming weight (GHW), has been applied to wiretap channel, network coding, linear ramp secret sharing, and trellis complexity, etc. Asymptotic analysis of RGHW is useful for investigating the optimal performance of these applications when code length is sufficiently large. For linear ramp secret sharing schemes, the asymptotic metric we previously introduced is inconvenient for characterizing its performance mainly because the rate of information leakage is not considered.In this paper, we improve the previous work by introducing two new asymptotic metrics, respectively, for the cases that r is fixed and r is proportionally increasing with n. For fixed r, we show the asymptotic Singleton, Plotkin and Gilbert-Varshamov bounds on the first metric. For increasing r, we determine the value of the second metric.
Published in: 2019 Ninth International Workshop on Signal Design and its Applications in Communications (IWSDA)
Date of Conference: 20-24 October 2019
Date Added to IEEE Xplore: 23 January 2020
ISBN Information: