BINARY CODES FROM THE GROUP PSU2(16)
Ali Zaghiyan, Ahmad Majlesi, Reza Kahkeshani, Hossein Shabani · 2014
In [1,2], Key and Moori considered the primitive actions of the Janko groups J1 and J2 and constructed designs , codes and graphs with J1 and J2 as a group of automorphisms . Together with Rodrigues , they extended the results of [1] by applying the same method to the groups PSpn(q) , A6 ≅ PSL2(9) and A9 in [3] . Their aim was to construct designs D from the action of a group G such that Aut(D) and Aut(G) have no containment relationship . In [4] , the authors considered the design D and binary code C constructed from the action of the McLaughlin group on 275 points and proved that Aut(C) = Aut(D) = ML:2 . Also , they examined some designs and their binary codes constructed from the primitive permutation representation of degree 2300 of the sporadic simple group Co2 [5] . Motivated by the method used in [1,2] , M . R . Darafsheh et al . considered all of the primitive actions of the groups PSL2(q) , q = 11 , 13 , 16 , 17 , 19 and 23 and found the parameters of all the designs and determined their automorphism groups [6] . These results were extended in [7] to the groups PSL2(q) , q = 8 , 25 , 27 , 29 , 31 and 32 and in [8] to the groups PSL2(q) , q = 37 , 41 , 43 , 47 and 49 . Therefore , the authors completed the construction of 1-designs using the primitive actions of the groups PSL2(q) , q a prime power less than 50 . Moreover , a certain 1−design D from the group PSL2(q) , q a power of 2 , are found such that Aut(D) ≅ Sq+1 [9] . In following , M . R . Darafsheh et al . constructed the binary