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An ever-widening workforce gap exists in the global cybersecurity industry but diverse talent is underutilized. The global cybersecurity workforce is only 25% female. Much research exists on the effect of gender bias on the hiring of women into the technical workforce, but little on how the gender of the recruiter (gender difference) affects recruitment decisions. This research reveals differences between the non-technical skills sought by female vs non-female cybersecurity recruiters. The former look for recruits with people-focused skills while the latter look for task-focused skills, highlighting the need for gender diversity in recruitment panels. Recruiters are increasingly seeking non-technical (soft) skills in technical graduate recruits. This requires STEM curriculum in Universities to adapt to match. Designing an industry-ready cybersecurity curriculum requires knowledge of these non-technical skills. An online survey of cybersecurity professionals was used to determine the most sought after non-technical skills in the field. Analysis of the data reveals distinct gender differences in the non-technical skills most valued in a recruit, based on the gender of the recruiter (not the recruited). The gender differences discovered do not correspond to the higher proportion of women employed in non-technical cybersecurity roles., Comment: 22 pages, 4 figures

An All-to-All Comparison problem is where every element of a data set is compared with every other element. This is analogous to projective planes and affine planes where every pair of points share a common line. For large data sets, the comparison computations can be distributed across a cluster of computers. All-to-All Comparison does not fit the highly successful Map-Reduce pattern, so a new distributed computing framework is required. The principal challenge is to distribute the data in such a way that computations can be scheduled where the data already lies. This paper uses projective planes, affine planes and balanced incomplete block designs to design data distributions and schedule computations. The data distributions based on these geometric and combinatorial structures achieve minimal data replication whilst balancing the computational load across the cluster.

Projective Hjelmslev planes and Affine Hjelmselv planes are generalisations of projective planes and affine planes. We present an algorithm for constructing a projective Hjelmslev planes and affine Hjelsmelv planes using projective planes, affine planes and orthogonal arrays. We show that all 2-uniform projective Hjelmslev planes, and all 2-uniform affine Hjelsmelv planes can be constructed in this way. As a corollary it is shown that all 2-uniform Affine Hjelmselv planes are sub-geometries of 2-uniform projective Hjelmselv planes., Comment: 15 pages. Algebraic Design Theory and Hadamard matrices, 2014, Springer Proceedings in Mathematics & Statistics 133

Sequences with optimal correlation properties are much sought after for applications in communication systems. In 1980, Alltop (IEEE Trans. Inf. Theory 26(3):350-354, 1980) described a set of sequences based on a cubic function and showed that these functions were optimal with respect to known bounds on auto and crosscorrelation. Subsequently these sequences were used to construct mutually unbiased bases, a structure of importance in quantum information theory. The key feature of this cubic function is that its difference function is a planar function. Functions with planar difference functions have been called \emph{Alltop functions}. This paper provides a new family of Alltop functions and establishes the use of Alltop functions for construction of sequence sets and MUBs., Comment: 15 pages

The projection construction has been used to construct semifields of odd characteristic using a field and a twisted semifield [Commutative semifields from projection mappings, Designs, Codes and Cryptography, 61 (2011), 187--196]. We generalize this idea to a projection construction using two twisted semifields to construct semifields of odd characteristic. Planar functions and semifields have a strong connection so this also constructs new planar functions.

Mutually unbiased bases (MUBs) have been used in several cryptographic and communications applications. There has been much speculation regarding connections between MUBs and finite geometries. Most of which has focused on a connection with projective and affine planes. We propose a connection with higher dimensional projective geometries and projective Hjelmslev geometries. We show that this proposed geometric structure is present in several constructions of MUBs., Comment: 5 pages. Accepted to ISIT2012

In 1980 Alltop produced a family of cubic phase sequences that nearly meet the Welch bound for maximum non-peak correlation magnitude. This family of sequences were shown by Wooters and Fields to be useful for quantum state tomography. Alltop's construction used a function that is not planar, but whose difference function is planar. In this paper we show that Alltop type functions cannot exist in fields of characteristic 3 and that for a known class of planar functions, $x^3$ is the only Alltop type function., Comment: Accepted to ISIT2012. v2 added a reference and adjusted margins

Given a finite associative ring with unity, $R$, and its two-dimensional left module, $^{2}R$, the following two problems are addressed: 1) the existence of vectors of $^{2}R$ that do not belong to any free cyclic submodule (FCS) generated by a unimodular vector and 2) conditions under which such (non-unimodular) vectors generate FCSs. The main result is that for a non-unimodular vector to generate an FCS of $^{2}R$, $R$ must have at least two maximal right ideals of which at least one is non-principal., Comment: 8 pages, no figures; V2 - some theorems slightly reworked, text polished and a reference added

This paper has been withdrawn by the author due to mathematical errors., Comment: This paper has been withdrawn