This paper addresses image copy detection, a task in online sharing platforms for copyright protection. While previous approaches have performed exceptionally well, the large size of their networks and descriptors remains a significant disadvantage, complicating their practical application. In this paper, we propose a novel method that achieves a competitive performance by using a lightweight network and compact descriptors. By utilizing relational self-supervised distillation to transfer knowledge from a large network to a small network, we enable the training of lightweight networks with a small descriptor size. Our approach, which we call Relational selfsupervised Distillation with Compact Descriptors (RDCD), introduces relational self-supervised distillation (RSD) for flexible representation in a smaller feature space and applies contrastive learning with a hard negative (HN) loss to prevent dimensional collapse. We demonstrate the effectiveness of our method using the DISC2021, Copydays, and NDEC benchmark datasets, with which our lightweight network with compact descriptors achieves a competitive performance. For the DISC2021 benchmark, ResNet-50/EfficientNet- B0 are used as a teacher and student respectively, the micro average precision improved by 5.0%/4.9%/5.9% for 64/128/256 descriptor sizes compared to the baseline method.