On Mathon's construction of maximal arcs in Desarguesian planes. II

In a recent paper [M], Mathon gives a new construction of maximal arcs which generalizes the construction of Denniston. In relation to this construction, Mathon asks the question of determining the largest degree of a non-Denniston maximal arc arising from his new construction. In this paper, we give a nearly complete answer to this problem. Specifically, we prove that when $m\geq 5$ and $m\neq 9$, the largest $d$ of a non-Denniston maximal arc of degree $2^d$ in PG(2,2^m) generated by a {p,1}-map is (\floor {m/2} +1). This confirms our conjecture in [FLX]. For {p,q}-maps, we prove that if $m\geq 7$ and $m\neq 9$, then the largest $d$ of a non-Denniston maximal arc of degree $2^d$ in PG(2,2^m) generated by a {p,q}-map is either \floor {m/2} +1 or \floor{m/2} +2.Comment: 21 page

Social reality and narrative form in the fiction of Henry Green

Social Reality and Narrative Form in the Fiction of Henry Green contests the dominant reading of Henry Green's fiction as an abstract, autonomous textual production. My thesis situates Green into a number of literary and socio-historical contexts and argues that doing so challenges a number of prevailing critical orthodoxies. I also argue that Green's fiction is formally constructed through a variety of dislocations, from displacing the centrality of plot, undermining the integrity of character, silencing the narrative voice and questioning the authenticity of the self. To relate social reality to narrative form, each of the four main chapters is dedicated to one of four substantive aspects of material reality: age, class, geography and the body. In the first chapter, I examine Green's relationship to the writing of his generation and to the concepts of age and youth. I argue that Green was deeply ambivalent towards generational belonging or the notion that identity could be supplied through one's generation. My second chapter investigates Green's treatment of social class and positions his Birmingham factory novel, Living, against 1930s theories of proletarian fiction and its canonical texts. My third chapter considers sites of authority both in the external world (geographic space) as well as within the novelistic space. The eclipsing of the narrator and the subsequent translation of the imaginative faculty to the reader is a part of Green's strategy to displace sites of authority. My final chapter looks at Green‘s treatment of the physical body and argues that disability is a central aspect of his novelistic practice. The impossibility of unity and wholeness, therefore, sheds light not only on the physicality of modern man but also on wholeness as a mental and linguistic possibility when the times are 'breaking up.'EThOS - Electronic Theses Online ServiceUniversity of WarwickGBUnited Kingdo

LDPC codes from Singer cycles

The main goal of coding theory is to devise efficient systems to exploit the full capacity of a communication channel, thus achieving an arbitrarily small error probability. Low Density Parity Check (LDPC) codes are a family of block codes--characterised by admitting a sparse parity check matrix--with good correction capabilities. In the present paper the orbits of subspaces of a finite projective space under the action of a Singer cycle are investigated.Comment: 11 Page