2015/11/09 by Jingjun Bao, Bao, Jingjun, Lijun Ji +1 · 1 citation
Computer Science · Engineering · Mathematics · #94A55 #94B25 #Algorithm #Block code #Coding theory and cryptography #Combinatorics #Computer science #Correlation #Discrete Mathematics (cs.DM) #Discrete mathematics #FOS: Computer and information sciences #Frequency-hopping spread spectrum #Hamming bound #Hamming code #Hamming distance #Hamming weight #Hamming(7,4) #Information Theory (cs.IT) #Mathematics #Partial correlation #Partition (number theory) #Telecommunications #Wireless Communication Networks Research #cs.DM #cs.IT #graph theory and CDMA systems #math.IT #msc:94A55 #msc:94B25
paper · pdf · doi:10.48550/arxiv.1511.02924
published in arXiv (Cornell University) (Cornell University) · 16 pages. arXiv admin note: text overlap with arXiv:1506.07372
openalex publication_date 2015/11/09 · arxiv created 2015/11/11 · arxiv updated 2015/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Frequency hopping sequences (FHSs) with favorable partial Hamming correlation properties have important applications in many synchronization and multiple-access systems. In this paper, we investigate constructions of FHSs and FHS sets with optimal partial Hamming correlation. We first establish a correspondence between FHS sets with optimal partial Hamming correlation and multiple partition-type balanced nested cyclic difference packings with a special property. By virtue of this correspondence, some FHSs and FHS sets with optimal partial Hamming correlation are constructed from various combinatorial structures such as cyclic difference packings, and cyclic relative difference families. We also describe a direct construction and two recursive constructions for FHS sets with optimal partial Hamming correlation. As a consequence, our constructions yield new FHSs and FHS sets with optimal partial Hamming correlation.