New Lower Bounds for Permutation Codes in the Ulam Metric
摘要
Permutation codes in the Ulam metric address translocation errors that arise in flash memories and powerline communications. We investigate the structure and construction of such codes, focusing on the maximum size P(n, d) of an (n, d)-permutation array. Some exact values of P(n, d) are determined. To improve scalability, we develop greedy constructions enhanced by prefix pruning and refined longest common subsequence analysis. These techniques improve the Gilbert—Varshamov lower bound and provide efficient algorithms for constructing larger codes.