scholarly journals Some Constant Weight Codes from Primitive Permutation Groups

10.37236/2702 ◽  
2012 ◽  
Vol 19 (4) ◽  
Author(s):  
Derek H. Smith ◽  
Roberto Montemanni
Keyword(s):  
Automorphism Group ◽  
Fixed Points ◽  
Maximum Clique ◽  
Permutation Groups ◽  
Linear Groups ◽  
Web Pages ◽  
Constant Weight Codes ◽  
Constant Weight ◽  
General Linear Groups

In recent years the detailed study of the construction of constant weight codes has been extended from length at most 28 to lengths less than 64. Andries Brouwer maintains web pages with tables of the best known constant weight codes of these lengths. In many cases the codes have more codewords than the best code in the literature, and are not particularly easy to improve. Many of the codes are constructed using a specified permutation group as automorphism group. The groups used include cyclic, quasi-cyclic, affine general linear groups etc. sometimes with fixed points. The precise rationale for the choice of groups is not clear.In this paper the choice of groups is made systematic by the use of the classification of primitive permutation groups. Together with several improved techniques for finding a maximum clique, this has led to the construction of 39 improved constant weight codes.

scholarly journals Unitary dual of GL(n) at archimedean places and global Jacquet–Langlands correspondence

2010 ◽  
Vol 146 (5) ◽  
pp. 1115-1164 ◽  
Author(s):  
A. I. Badulescu ◽  
D. Renard
Keyword(s):  
General Linear ◽  
Linear Groups ◽  
Automorphic Representations ◽  
Langlands Correspondence ◽  
General Linear Groups ◽  
Multiplicity One ◽  
Unitary Dual ◽  
Strong Multiplicity ◽  
Local Results

AbstractIn a paper by Badulescu [Global Jacquet–Langlands correspondence, multiplicity one and classification of automorphic representations, Invent. Math. 172 (2008), 383–438], results on the global Jacquet–Langlands correspondence, (weak and strong) multiplicity-one theorems and the classification of automorphic representations for inner forms of the general linear group over a number field were established, under the assumption that the local inner forms are split at archimedean places. In this paper, we extend the main local results of that article to archimedean places so that the above condition can be removed. Along the way, we collect several results about the unitary dual of general linear groups over ℝ, ℂ or ℍ which are of independent interest.

scholarly journals The Classification of Permutation Groups with Maximum Orbits

2018 ◽  
Vol 15 ◽  
pp. 8155-8161
Author(s):  
Behname Razzaghmaneshi
Keyword(s):  
Positive Integer ◽  
Fixed Points ◽  
Permutation Group ◽  
Permutation Groups

Let G be a permutation group on a set with no fixed points in and let m be a positive integer. If no element of G moves any subset of by more than m points (that is, if for every and g 2 G), and the lengths two of orbits is p, and the restof orbits have lengths equal to 3. Then the number t of G-orbits in is at most  Moreover, we classifiy all groups for is hold.(For  denotes the greatest integer less than or equal to x.)

scholarly journals DECOMPOSITION THEOREMS FOR AUTOMORPHISM GROUPS OF TREES

2020 ◽  
pp. 1-9
Author(s):  
MAX CARTER ◽  
GEORGE A. WILLIS
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Continuous Homomorphism ◽  
Local Fields ◽  
General Linear ◽  
Linear Groups ◽  
Closed Range ◽  
Regular Tree ◽  
General Linear Groups ◽  
Decomposition Theorems

Motivated by the Bruhat and Cartan decompositions of general linear groups over local fields, we enumerate double cosets of the group of label-preserving automorphisms of a label-regular tree over the fixator of an end of the tree and over maximal compact open subgroups. This enumeration is used to show that every continuous homomorphism from the automorphism group of a label-regular tree has closed range.

New constant weight codes from linear permutation groups

1997 ◽  
Vol 43 (5) ◽  
pp. 1623-1630 ◽  
Author(s):  
K.J. Nurmela ◽  
M.K. Kaikkonen ◽  
P.R.J. Ostergard
Keyword(s):  
Permutation Groups ◽  
Constant Weight Codes ◽  
Constant Weight
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