2008/01/25 by Lizhen Yang, Yang, Lizhen, Kefei Chen +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Mathematics · #Cellular Automata and Applications #DNA and Biological Computing #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #graph theory and CDMA systems #math.IT
paper · pdf · doi:10.48550/arxiv.0801.3986
arxiv created 2008/01/25 · openalex publication_date 2008/01/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A permutation array(or code) of length n and distance d, denoted by (n,d) PA, is a set of permutations C from some fixed set of n elements such that the Hamming distance between distinct members x,y∈ C is at least d. Let P(n,d) denote the maximum size of an (n,d) PA. This correspondence focuses on the lower bound on P(n,d). First we give three improvements over the Gilbert-Varshamov lower bounds on P(n,d) by applying the graph theorem framework presented by Jiang and Vardy. Next we show another two new improved bounds by considering the covered balls intersections. Finally some new lower bounds for certain values of n and d are given.