Determining when the absolute state complexity of a Hermitian code achieves its DLP bound

Let g be the genus of the Hermitian function field H/F(q)2 and let C-L(D,mQ(infinity)) be a typical Hermitian code of length n. In [Des. Codes Cryptogr., to appear], we determined the dimension/length profile (DLP) lower bound on the state complexity of C-L(D,mQ(infinity)). Here we determine when this lower bound is tight and when it is not. For m less than or equal to n-2/2 or m greater than or equal to n-2/2 + 2g, the DLP lower bounds reach Wolf's upper bound on state complexity and thus are trivially tight. We begin by showing that for about half of the remaining values of m the DLP bounds cannot be tight. In these cases, we give a lower bound on the absolute state complexity of C-L(D,mQ(infinity)), which improves the DLP lower bound. Next we give a good coordinate order for C-L(D,mQ(infinity)). With this good order, the state complexity of C-L(D,mQ(infinity)) achieves its DLP bound (whenever this is possible). This coordinate order also provides an upper bound on the absolute state complexity of C-L(D,mQ(infinity)) (for those values of m for which the DLP bounds cannot be tight). Our bounds on absolute state complexity do not meet for some of these values of m, and this leaves open the question whether our coordinate order is best possible in these cases. A straightforward application of these results is that if C-L(D,mQ(infinity)) is self-dual, then its state complexity (with respect to the lexicographic coordinate order) achieves its DLP bound of n /2 - q(2)/4, and, in particular, so does its absolute state complexity.

Lower Bounds on the State Complexity of Geometric Goppa Codes

We reinterpret the state space dimension equations for geometric Goppa codes. An easy consequence is that if deg G less than or equal to n-2/2 or deg G greater than or equal to n-2/2 + 2g then the state complexity of C-L(D, G) is equal to the Wolf bound. For deg G is an element of [n-1/2, n-3/2 + 2g], we use Clifford's theorem to give a simple lower bound on the state complexity of C-L(D, G). We then derive two further lower bounds on the state space dimensions of C-L(D, G) in terms of the gonality sequence of F/F-q. (The gonality sequence is known for many of the function fields of interest for defining geometric Goppa codes.) One of the gonality bounds uses previous results on the generalised weight hierarchy of C-L(D, G) and one follows in a straightforward way from first principles; often they are equal. For Hermitian codes both gonality bounds are equal to the DLP lower bound on state space dimensions. We conclude by using these results to calculate the DLP lower bound on state complexity for Hermitian codes.

Checklist of health promotion environments at worksites (CHEW): Development and measurement characteristics

Purpose. Health promotion policy frameworks, recent theorizing, and research all emphasize understanding and mobilizing environmental influences to change particular health-related behaviors in specific settings. The workplace is a key environmental setting. The Checklist of Health Promotion Environments at Worksites (CHEW) was designed as a direct observation instrument to assess characteristics of worksite environments that are known to influence health-related behaviors. Methods. The CHEW is a 112-item checklist of workplace environment features hypothesized to be associated, both positively and negatively, with physical activity, healthy eating, alcohol consumption, and smoking. The three environmental domains assessed are (1) physical characteristics of the worksite, (2) features of the information environment, and (3) characteristics of the immediate neighborhood around the workplace. The conceptual rationale and development studies for the CHEW are described, and data from observational studies of 20 worksites are reported. Results. The data on CHEW-derived environmental attributes showed generally good reliability and identified meaningful sets of variables that plausibly may influence health-related behaviors. With the exception of one information environment attribute, intraclass correlation coefficients ranged from 0.80 to 1.00. Descriptive statistics on selected physical and information environment characteristics indicated that vending machines, showers, bulletin boards, and signs prohibiting smoking were common across worksites. Bicycle racks, visible stairways, and signs related to alcohol consumption, nutrition, and health. promotion were relatively uncommon. Conclusions. These findings illustrate the types of data on environmental attributes that can be derived, their relevance for program planning, and how they can characterize variability across worksites. The CHEW is a promising observational measure that has the potential to assess environmental influences on health behaviors and to evaluate workplace health promotion programs.

Conceptions of health and illness held by Australian Aboriginal, Torres Strait Islander and Papua New Guinea Health Science students

Health is considered to be a fundamental human right and developing a better understanding of health is assumed to be a global social goal (Bloom, 1987). Yet many third-world countries and some subpopulations within developed countries do not enjoy a healthy existence. The research reported in this paper examined the conceptions of health and conceptions of illness for a group of Aboriginal, Torres Strait Islander, and Papua New Guinea university students studying health science courses. Results found three conceptions of health and three conceptions of illness that indicated these students held a mix of traditional cultural and Western beliefs. These findings may contribute to overcoming the dissonance between traditional and Western beliefs about health and the development of health care courses that are more specific to how these students understand health. This may also serve to improve the educational status of Aboriginal and Torres Strait Islander people and potentially improve the health status within these communities.