On Asymptotic Analysis of Relative Generalized Hamming Weight The relative generalized Hamming weight (RGHW) M r (C,C1) of an n, k (linear) code C and an n, k 1  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 GilbertVarshamov bounds on the first metric. For increasing r, we determine the value of the second metric.

Multilibrary Coded Caching with Partial Secrecy The paper considers a coded caching setup with two libraries and where only one of them needs to be kept secret from an external eavesdropper. We provide upper and lower bounds on the secrecy ratememory tradeoff for systems with mathsfK  2 or mathsfK  3 receivers. Our bounds are tight in some regimes and show that the standard (nonsecure) coded caching upper bound can be approached for a wide range of parameters. In some cases, the proposed upper bound on the secrecy ratememory tradeoff is even lower than the lower bound for standard coded caching. The reason is that in our setup the ratio of receivers requesting secure files over those requesting nonsecure files is fixed and known to everyone in advance. The transmitter can thus adjust the contents stored in the cache memories to this ratio.