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.

Monostephanostomum georgianum n. sp (Digenea : Acanthocolpidae) from Arripis georgianus (Valenciennes) (Perciformes : Arripidae) off Kangaroo Island, South Australia, with comments on Monostephanostomum Kruse, 1979 and Stephanostomum Looss, 1899

Monostephanostomum georgianum n. sp. is described from Arripis georgianus off Kangaroo Island, South Australia. It differs from its congeners by the presence of a short second row of oral spines. M. manteri Kruse, 1979 is reported from A. georgianus off southern Western Australia and Kangaroo Island, South Australia and A. trutta off northern Tasmania. It is considered that the other two species, M. yamagutii Ramadan, 1984 and M. krusei Reimer, 1983, should probably be removed from this genus. Two new combinations are formed, M. gazzae (Shen, 1990) n. comb. (from Stephanostomum) and M. mesospinosum (Madhavi, 1976) n. comb. (from Stephanostomum). A key to the four recognised species of Monostephanostomum is given.

A new subfamily, Bothriocrotoninae n. subfam., for the genus Bothriocroton Keirans, King & Sharrad, 1994 status amend. (Ixodida : Ixodidae), and the synonymy of Aponomma Neumann, 1899 with Amblyomma Koch, 1844

Evidence suggesting polyphyly of the traditionally recognised tick genus Aponomma Neumann, 1899 is summarized. Continued recognition of this genus in its current concept leaves a polyphyletic genus Aponomma and a paraphyletic genus Amblyomma Koch, 1844. To improve the correlation between our understanding of phylogenetic relationships in metastriate ticks and their classification, a few changes in classification are proposed. The members of the 'indigenous Australian Aponomma' group (sensu Kaufman, 1972), A. auruginans Schulze, 1936, A. concolor Neumann, 1899, A. glebopalma Keirans, King & Sharrad, 1994, A. hydrosauri (Denny, 1843) and A. undatum (Fabricius, 1775), are transferred to Bothriocroton Keirans, King & Sharrad, 1994, which is raised to full generic rank. The remaining members of Aponomma are transferred to Amblyomma. Uncertainty remains on relationships of Bothriocroton to other metastriate lineages and on the systematic position of the two species formerly included in the 'primitive Aponomma' group, A. elaphense Price, 1959 and A. sphenodonti Dumbleton, 1943.

Species of Stephanostomum Looss, 1899 (Digenea : Acanthocolpidae) from fishes of Australian and South Pacific waters, including five new species

Nine species of Stephanostomum are described from Australian and Southern Pacific marine fishes: Stephanostomum madhaviae n. sp. [syn. S. orientalis of Madhavi ( 1976)] from Caranx ignobilis, off Hope Island, Queensland, with 30-34 circum-oral spines and vitelline fields almost reaching to the posterior extremity of the cirrus-sac; S. bicoronatum (Stossich, 1883) from Argyrosomus hololepidotus, off Southport Broadwater, Queensland; S. votonimoli n. sp. from Scomberoides lysan, off Moorea, French Polynesia ( type-locality) and Western Samoa, with 33-38 circum-oral spines, a uroproct and the vitelline fields not reaching the cirrus-sac; S. nyoomwa n. sp. from Caranx sexfasciatus, off Heron Island, Queensland, with 33-38 circum-oral spines, a uroproct and the vitelline fields reaching the cirrus-sac; S. cobia n. sp. from Rachycentron canadum, off Heron Island, with 36 circum-oral spines, a uroproct and the vitelline fields reaching the cirrus-sac; S. petimba Yamaguti, 1970 from Seriola hippos, off Rottnest Island, Western Australia; S. pacificum ( Yamaguti, 1951) from Pseudocaranx wrighti, off Fremantle, Western Australia; S. aaravi n. sp. from Lethrinus miniatus, off Heron Island, with 36-39 circumoral spines, probably a uroproct and the vitelline fields reaching the ventral sucker; S. pagrosomi ( Yamaguti, 1939) from L. nebulosus, L. miniatus and L. atkinsoni off Heron Island, Pagrus auratus, off Rottnest Island, Western Australia and Gymnocranius audleyi, off Heron Island. A digest of described species of Stephanostomum is included as an appendix.