Abstract. Through a modular representation theoretical approach we enumerate all non-trivial code... more Abstract. Through a modular representation theoretical approach we enumerate all non-trivial codes from the 2-modular representations of A8, using a chain of maximal submodules of a permutation module induced by the action of A8 on objects such as points, Steiner S (3, 4, 8) systems, duads, bisections and triads. Using the geometry of these objects we attempt to gain some insight into the nature of possible codewords, particularly those of minimum weight.
Abstract We examine the p-ary codes, for any prime p, from the row span over F _p of| V|×| E| inc... more Abstract We examine the p-ary codes, for any prime p, from the row span over F _p of| V|×| E| incidence matrices of connected graphs Γ=(V, E), showing that certain properties of the codes can be directly derived from the parameters and properties of the graphs.
In their natural primitive rank-3 action on the singular and non-singular points of the projectiv... more In their natural primitive rank-3 action on the singular and non-singular points of the projective space of dimension 2 m− 1, the simple orthogonal groups O∊ 2 m (F2), for∊=±1 and m≥ 3 have 2-modular representations that give rise to self-orthogonal binary codes whose properties can be linked to those of the underlying geometry. We describe the structures of the stabilizers of the codewords of any given non-zero weight in the codes. Moreover we show that the codewords of any given non-zero weight are single orbits ...
A drug use epidemic can be represented by a finite number of states and transition rules that gov... more A drug use epidemic can be represented by a finite number of states and transition rules that govern the dynamics of drug use in each discrete time step. This paper investigates the spread of drug use in a community where some users are in treatment and others are not in treatment, citing South Africa as an example. In our analysis, we consider the neighbourhood prevalence of each individual, ie, the proportion of the individual's drug user contacts who are not in treatment amongst all of his or her contacts. We introduce ...
Discrete mathematics has had many applications in recent years and this is only one reason for it... more Discrete mathematics has had many applications in recent years and this is only one reason for its increasing dynamism. The study of finite structures is a broad area which has a unity not merely of description but also in practice, since many of the structures studied give results which can be applied to other, apparently dissimilar structures. Apart from the applications, which themselves generate problems, internally there are still many difficult and interesting problems in finite geometry and combinatorics. There are still many ...
Abstract. Through a modular representation theoretical approach we enumerate all non-trivial code... more Abstract. Through a modular representation theoretical approach we enumerate all non-trivial codes from the 2-modular representations of A8, using a chain of maximal submodules of a permutation module induced by the action of A8 on objects such as points, Steiner S (3, 4, 8) systems, duads, bisections and triads. Using the geometry of these objects we attempt to gain some insight into the nature of possible codewords, particularly those of minimum weight.
Abstract We examine the p-ary codes, for any prime p, from the row span over F _p of| V|×| E| inc... more Abstract We examine the p-ary codes, for any prime p, from the row span over F _p of| V|×| E| incidence matrices of connected graphs Γ=(V, E), showing that certain properties of the codes can be directly derived from the parameters and properties of the graphs.
In their natural primitive rank-3 action on the singular and non-singular points of the projectiv... more In their natural primitive rank-3 action on the singular and non-singular points of the projective space of dimension 2 m− 1, the simple orthogonal groups O∊ 2 m (F2), for∊=±1 and m≥ 3 have 2-modular representations that give rise to self-orthogonal binary codes whose properties can be linked to those of the underlying geometry. We describe the structures of the stabilizers of the codewords of any given non-zero weight in the codes. Moreover we show that the codewords of any given non-zero weight are single orbits ...
A drug use epidemic can be represented by a finite number of states and transition rules that gov... more A drug use epidemic can be represented by a finite number of states and transition rules that govern the dynamics of drug use in each discrete time step. This paper investigates the spread of drug use in a community where some users are in treatment and others are not in treatment, citing South Africa as an example. In our analysis, we consider the neighbourhood prevalence of each individual, ie, the proportion of the individual's drug user contacts who are not in treatment amongst all of his or her contacts. We introduce ...
Discrete mathematics has had many applications in recent years and this is only one reason for it... more Discrete mathematics has had many applications in recent years and this is only one reason for its increasing dynamism. The study of finite structures is a broad area which has a unity not merely of description but also in practice, since many of the structures studied give results which can be applied to other, apparently dissimilar structures. Apart from the applications, which themselves generate problems, internally there are still many difficult and interesting problems in finite geometry and combinatorics. There are still many ...
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Papers by Bernardo Rodrigues