Peer review is a common process for evaluating paper submissions and selecting high-quality papers at academic conferences. A significant task is assigning submissions to appropriate reviewers. Considering the constraints of reviewers, papers, and conflicts of interest, retrieval-based methods and assignment-based methods were proposed in previous works. However, an author could also be a reviewer in the conference. The loops between authors and reviewers may cause cooperative cheating. In this paper, two algorithms are proposed for a k-loop free assignment, which ensures the loop length is no less than k. Inspired by the existing works, the first algorithm assigns reviewers to maximize the summation of suitability scores, temporarily ignoring the k-loop free constraint. Afterward, the loops are detected and adjusted based on mergers. The second algorithm generates k-loop free assignments within the nodes that are both reviewers and authors. The other assignments are generated using linear programming. Extensive experiments show the effectiveness of the proposed methods.