Designs and codes from involutions of An

We previously have developed two methods for constructing codes and designs from finite simple groups. In a recent paper we introduced a new method (Method 3) for constructing codes and designs from fixed points of elements of finite transitive groups. This new method together with background material and results required from finite groups, permutation groups and representation theory were discussed fully in that paper. The main aim of this paper is to apply the method to the fixed points of involutions of the Alternating group An (for ≥ 5) on its action on Ω, 2-subsets (or duads) Γ{2} of a set Γ of size n

Fischer-Clifford matices of the non-split group extension 26·U4(2)

Click on the link to view the abstract.Keywords: Fischer-Clifford matrices, Harada-Norton group, sporadic simple group, maximal subgroup, non-split extensionQuaestiones Mathematicae 31(2008), 27–3

On the ranks of Janko groups J1, J2, J3 and J4

If G is a finite group and X a conjugacy class of elements of G, then we define rank (G : X) to be the minimum number of elements of X generating G. In the present paper we study the rank(Ji : X) for all conjugacy classes of Ji, where i = 1, 2, 3, 4.Keywords: Janko groups, rank, simple groups, sporadic groupsQuaestiones Mathematicae 31(2008), 37–4

Permutation decoding for the binary codes from triangular graphs

AbstractBy finding explicit PD-sets we show that permutation decoding can be used for the binary code obtained from an adjacency matrix of the triangular graph T(n) for any n≥5

Ternary codes from graphs on triples

AbstractFor a set Ω of size n≥7 and Ω{3} the set of subsets of Ω of size 3, we examine the ternary codes obtained from the adjacency matrix of each of the three graphs with vertex set Ω{3}, with adjacency defined by two vertices as 3-sets being adjacent if they have zero, one or two elements in common, respectively