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.

Fresh-state properties of self-compacting mortar and concrete with combined use of limestone filler and fly ash

This paper presents the results of a study on the behaviour of self-compacting concrete (SCC) in the fresh and hardened states, produced with binary and ternary mixes of fly ash (FA) and limestone filler (LF), using the method proposed by Nepomuceno. His method determines the SCC composition parameters in the mortar phase (self-compacting mortar - SCM) easily and efficiently, whilst guaranteeing the SCC properties in both the fresh and hardened states. For this, 11 SCMs were studied: one with cement (C) only; three with FA at 30%, 60% and 70% C substitution; three with LF at 30%, 60% and 70% C substitution; four with FA + LF in combinations of 10-20%, 20-10%, 20-40% and 40-20% C substitution. Once the composition of these mortars was defined, 18 SCC mixes were produced: 14 binary SCC mixes were produced with the seven binary mortar mixes, and four ternary SCC mixes were produced with the four ternary mortar mixes. In addition to the methodology proposed by Nepomuceno, the combined use of FA and LF in ternary mixtures was tested. The results confirmed that the method could yield SCC with adequate properties in both the fresh and hardened states. It was also possible to determine the SCC composition parameters in the mortar phase (self-compacting mortar - SCM) that will guarantee the SCC properties in both the fresh and hardened states, as confirmed through the optimized behaviour of the SCC in the fresh state and the promising results in the hardened state (compressive strength). The potential demonstrated by the joint use of LF and FA through the synergetic interaction of both additions is emphasized.

An Investigation into Irish State patronage of the visual arts.

The focus of this research is in ascertaining how and why the Irish state patronises the visual arts. The framework that the state puts in place for the support of the arts influences the creation of art. The initial standpoint from which to evaluate the system is founded on the belief that art is of social good. The second source of belief is in the necessity for an autonomous setting in which it can be created. These two beliefs underpin state patronage of the arts in contemporary society. Therefore they have to be examined carefully in order to see if they hold up. This requires an investigation into the formation of value. This is undertaken by looking into the social development of western society and its influence on the placement of arts value. Establishing how arts value to society is defined provides a means by which to investigate the manner in which the state patronises the visual arts. Two case studies provide the evidence in how the state supports the arts and why it chooses to do so. The Irish Museum of Modem Art is used as an example of the state’s role in the maintenance of the canon of art. The second case study looks at the work being done by Breaking Ground. Breaking Ground is an extensive art project as an element of the regeneration process happening in Ballymun funded by the state. It provides and insight into how the state utilises art in the unification of a social group.

Report of the State board of agriculture on the work of extermination of the gypsy moth.

1898:Jan.

Report of the State board of agriculture on the work of extermination of the gypsy moth.

1897:Jan.

Fishery bulletin / U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, National Marine Fisheries Service.

v.81 (1983)

Fishery bulletin / U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, National Marine Fisheries Service.

v.91 (1993)

Fishery bulletin / U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, National Marine Fisheries Service.

v.74 (1976)

Fishery bulletin / U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, National Marine Fisheries Service.

v.71 (1973)

Fishery bulletin / U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, National Marine Fisheries Service.

v.69 (1971)

Fishery bulletin / U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, National Marine Fisheries Service.

v.73 (1975)

Fishery bulletin / U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, National Marine Fisheries Service.

v.72 (1974)