Characterisation of a family of neighbour transitive codes

We consider codes of length $m$ over an alphabet of size $q$ as subsets of the vertex set of the Hamming graph $\Gamma=H(m,q)$. A code for which there exists an automorphism group $X\leq Aut(\Gamma)$ that acts transitively on the code and on its set of neighbours is said to be neighbour transitive, and were introduced by the authors as a group theoretic analogue to the assumption that single errors are equally likely over a noisy channel. Examples of neighbour transitive codes include the Hamming codes, various Golay codes, certain Hadamard codes, the Nordstrom Robinson codes, certain permutation codes and frequency permutation arrays, which have connections with powerline communication, and also completely transitive codes, a subfamily of completely regular codes, which themselves have attracted a lot of interest. It is known that for any neighbour transitive code with minimum distance at least 3 there exists a subgroup of $X$ that has a $2$-transitive action on the alphabet over which the code is defined. Therefore, by Burnside's theorem, this action is of almost simple or affine type. If the action is of almost simple type, we say the code is alphabet almost simple neighbour transitive. In this paper we characterise a family of neighbour transitive codes, in particular, the alphabet almost simple neighbour transitive codes with minimum distance at least $3$, and for which the group $X$ has a non-trivial intersection with the base group of $Aut(\Gamma)$. If $C$ is such a code, we show that, up to equivalence, there exists a subcode $\Delta$ that can be completely described, and that either $C=\Delta$, or $\Delta$ is a neighbour transitive frequency permutation array and $C$ is the disjoint union of $X$-translates of $\Delta$. We also prove that any finite group can be identified in a natural way with a neighbour transitive code.Comment: 30 Page

Twisted Permutation Codes

We introduce twisted permutation codes, which are frequency permutation arrays analogous to repetition permutation codes, namely, codes obtained from the repetition construction applied to a permutation code. In particular, we show that a lower bound for the minimum distance of a twisted permutation code is the minimum distance of a repetition permutation code. We give examples where this bound is tight, but more importantly, we give examples of twisted permutation codes with minimum distance strictly greater than this lower bound.Comment: 20 page

Elusive Codes in Hamming Graphs

We consider a code to be a subset of the vertex set of a Hamming graph. We examine elusive pairs, code-group pairs where the code is not determined by knowledge of its set of neighbours. We construct a new infinite family of elusive pairs, where the group in question acts transitively on the set of neighbours of the code. In our examples, we find that the alphabet size always divides the length of the code, and prove that there is no elusive pair for the smallest set of parameters for which this is not the case. We also pose several questions regarding elusive pairs

Conway groupoids, regular two-graphs and supersimple designs

A $2-(n,4,\lambda)$ design $(\Omega, \mathcal{B})$ is said to be supersimple if distinct lines intersect in at most two points. From such a design, one can construct a certain subset of Sym$(\Omega)$ called a "Conway groupoid". The construction generalizes Conway's construction of the groupoid $M_{13}$. It turns out that several infinite families of groupoids arise in this way, some associated with 3-transposition groups, which have two additional properties. Firstly the set of collinear point-triples forms a regular two-graph, and secondly the symmetric difference of two intersecting lines is again a line. In this paper, we show each of these properties corresponds to a group-theoretic property on the groupoid and we classify the Conway groupoids and the supersimple designs for which both of these two additional properties hold.Comment: 17 page

Hyperon production in near threshold nucleon-nucleon collisions

We study the mechanism of the associated Lambda-kaon and Sigma-kaon production in nucleon-nucleon collisions over an extended range of near threshold beam energies within an effective Lagrangian model, to understand of the new data on pp --> p Lambda K+ and pp --> p Sigma0 K+ reactions published recently by the COSY-11 collaboration. In this theory, the hyperon production proceeds via the excitation of N*(1650), N*(1710), and N*(1720) baryonic resonances. Interplay of the relative contributions of various resonances to the cross sections, is discussed as a function of the beam energy over a larger near threshold energy domain. Predictions of our model are given for the total cross sections of pp --> p Sigma+K0, pp --> n Sigma+K+, and pn --> n Lambda K+ reactions.Comment: 16 pages, 4 figures, one new table added and dicussions are updated, version accepted for publication by Physical Review

Demographic Understanding of Volunteerism

A large sample of volunteers from a midwestern city chapter of the American Red Cross were studied to identify demographic correlates of the reasons given for volunteering. The findings suggest that the reasons people give for doing volunteer work are conditioned by their age, sex, and marital status. Implications for volunteer programs and future research are discussed

On the master equation approach to diffusive grain-surface chemistry: the H, O, CO system

We have used the master equation approach to study a moderately complex network of diffusive reactions occurring on the surfaces of interstellar dust particles. This network is meant to apply to dense clouds in which a large portion of the gas-phase carbon has already been converted to carbon monoxide. Hydrogen atoms, oxygen atoms, and CO molecules are allowed to accrete onto dust particles and their chemistry is followed. The stable molecules produced are oxygen, hydrogen, water, carbon dioxide (CO2), formaldehyde (H2CO), and methanol (CH3OH). The surface abundances calculated via the master equation approach are in good agreement with those obtained via a Monte Carlo method but can differ considerably from those obtained with standard rate equations.Comment: 13 pages, 5 figure