New Bounds on the Partial Hamming Correlation of WideGap FrequencyHopping Sequence Sets* In frequencyhopping systems, there should be a wide frequencyhopping gap between two adjacent frequencies in case the received signals are prone to be interfered by staying at one frequency point for a long time. In this paper, a bound on the maximum partial Hamming autocorrelation of widegap frequencyhopping sequence (WGFHS) and two bounds on the maximum partial Hamming correlation of WGFHS sets are discussed. Moreover, the proposed bounds are tighter than the existing EunJinHongSong bound and ZhouTangNiuUdaya bounds in the sense that they can be achieved by the parameters of some WGFHSs and they are obtained in the literature for the first time.

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.