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

Do the Poor Pay More for Healthy Food? An Empirical Economic Analysis

Food Consumption/Nutrition/Food Safety,

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

Consumer-Preferred Attributes of a Fresh Ground Beef and Turkey Product: A Conjoint Analysis

A random sample of 3,400 Louisiana households was surveyed by mail to determine their ratings for a number of product profiles involving a combined fresh ground beef and turkey product. The attributes and levels of the new product included form (fresh, frozen), identity of the packager (retailer, processor), percentage of beef in product (50,70,90), and price of the combined product as a percentage of ground beef (80,90,100). Based on 2,781 observations, the order of importance of the attributes were, in order of declining importance, content, form, price, and packager. Consumer utility was highly sensitive to the content of beef, with a higher content being preferred.Consumer/Household Economics,

New characterisations of the Nordstrom–Robinson codes

In his doctoral thesis, Snover proved that any binary $(m,256,\delta)$ code is equivalent to the Nordstrom-Robinson code or the punctured Nordstrom-Robinson code for $(m,\delta)=(16,6)$ or $(15,5)$ respectively. We prove that these codes are also characterised as \emph{completely regular} binary codes with $(m,\delta)=(16,6)$ or $(15,5)$, and moreover, that they are \emph{completely transitive}. Also, it is known that completely transitive codes are necessarily completely regular, but whether the converse holds has up to now been an open question. We answer this by proving that certain completely regular codes are not completely transitive, namely, the (Punctured) Preparata codes other than the (Punctured) Nordstrom-Robinson code

Evaluating the effects of turf-replacement programs in Los Angeles

Water utilities incentivize turf replacement to promote water conservation, but the effects of such programs have received limited evaluations. In 2014, the Metropolitan Water District of Southern California (MWD) undertook an unprecedented investment to incentive turf replacement throughout Southern California in response to a serious Statewide drought. MWD devoted $350 million to the program, resulting in more than 46,000 rebate payments (25,000 in Los Angeles County) to remove 15.3 million square meters of turf. The program implementation provided a unique opportunity to address research gaps on turf replacement implementation. We analyzed socioeconomic and spatial trends of program participants and assessed landscape changes from turf replacement using a random sample of properties (4% of LA County participants in 2014–16). Specifically, we used a novel and cost-effective approach Google Earth Street View to characterize landscapes in front yards and created a typology of land cover types. Results showed: post-replacement landscapes had a diversity of land cover types – diverse yards with several land cover types, as well as more homogenous yards with a single land cover such as woodchips, bare soil, gravel, and artificial turf. Analysis also indicated some evidence of “neighborhood adoption” effects. We describe the need for longitudinal studies to understand long-term effects of turf replacement and associated water use, and suggest that water utilities should also evaluate results in backyards, which requires site visits. This study provides a novel contribution that can be replicated over space and time to further knowledge of turf replacement program implementations and evaluation