2020/12/04 by Ganzhinov Mikhail, Mikhail, Ganzhinov · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Antenna and Metasurface Technologies #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Functional Analysis (math.FA) #Structural Analysis and Optimization #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2012.02718
openalex publication_date 2020/12/04 · openalex created_date 2022/07/13 · openalex updated_date 2026/07/28
A line packing is optimal if its coherence is as small as possible. Most\ninteresting examples of optimal line packings are achieving equality in some of\nthe known lower bounds for coherence. In this paper two infinite families of\nreal and complex biangular line packings are presented. New packings achieve\nequality in the real or complex second Levenshtein bound respectively. Both\ninfinite families are constructed by analyzing well known representations of\nthe finite groups SL(2, mathbbFq). Until now the only known infinite\nfamiles meeting the second Levenshtein bounds were related to the maximal sets\nof mutually unbiased bases (MUB). Similarly to the line packings related to the\nmaximal sets of MUBs, the line packings presented here are related to the\nmaximal sets of mutually unbiased weighing matrices. Another similarity is that\nthe new packings are projective 2-designs. The latter property together with\nsufficiently large cardinalities of the new packings implies some improvement\non largest known cardinalities of real and complex biangular tight frames.\n