2016/11/22 by Xin Wang, Yiwei Zhang, Wang, Xin +5
Computer Science · Engineering · #Advanced Wireless Communication Techniques #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1611.07188
openalex publication_date 2016/11/22 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
Permutation codes are widely studied objects due to their numerous applications in various areas, such as power line communications, block ciphers, and the rank modulation scheme for flash memories. Several kinds of metrics are considered for permutation codes according to their specific applications. This paper concerns some improvements on the bounds of permutation codes under Hamming metric and Kendall's τ-metric respectively, using mainly a graph coloring approach. Specifically, under Hamming metric, we improve the Gilbert-Varshamov bound asymptotically by a factor n, when the minimum Hamming distance d is fixed and the code length n goes to infinity. Under Kendall's τ-metric, we narrow the gap between the known lower bounds and upper bounds. Besides, we also obtain some sporadic results under Kendall's τ-metric for small parameters.