On the support weight distributions of relative subcodes of some classes of codes

Relative subcodes of a code can be used to describe the security of the un-leaked data symbols in the wire-tap channel with multi-users. In particular, the relative generalized Hamming weight is determined by the minimum support weight of the relative subcodes. We determine the support weight distributions of relative subcodes of several classes of optimal codes which were constructed recently by the down-sets. With respect to certain subcodes with any dimension, the relative generalized Hamming weights of each class of optimal codes are completely determined by using the obtained support weight distributions of relative subcodes. We also show that the relative generalized Hamming weights of each class of optimal codes always achieve the so-called RCW upper bound except few cases.