TY - JOUR
AU1 - Moori, Jamshid
AB - In this paper, we aim to study maximal pairwise commuting sets of 3-transpositions, and to construct designs and codes from these sets. Any maximal set of pairwise 3-transpositions is called a basic set of transpositions. Let G be a 3-transposition group with the set D as the conjugacy class consisting of its 3-transpositions. Let L be a set of basic transpositions in D. We aim to give a general description of 1-(v,k,λ)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$(v,k,\lambda )$$\end{document} designs D=(P,B)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathcal {D}}=(\mathcal {P}, \mathcal {B})$$\end{document}, with P=D\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal {P}=D$$\end{document} and B={Lg|g∈G}.\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal {B}=\{L^g|g\in G\}.$$\end{document} The parameters k=|L|\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$k=|L|$$\end{document}, λ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\lambda $$\end{document} and further properties of D\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathcal {D}}$$\end{document} are determined. In addition, some of the codes associated with these designs are also discussed. We also, as examples, apply the method to Symmetric groups Sn\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$S_n$$\end{document} and Fischer groups Fi\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$F_i$$\end{document} for i∈{21,22,23,24}\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$i\in \{21, 22, 23, 24\}$$\end{document}.
TI - Designs and Codes from Basic 3-Transpositions
JF - Bulletin of the Iranian Mathematical Society
DO - 10.1007/s41980-021-00673-w
DA - 2022-10-01
UR - https://www.deepdyve.com/lp/springer-journals/designs-and-codes-from-basic-3-transpositions-vaBg98eiMr
SP - 2855
EP - 2871
VL - 48
IS - 5
DP - DeepDyve
ER -