Additive Asymmetric Quantum Codes

We present a general construction of asymmetric quantum codes based on additive codes under the trace Hermitian inner product. Various families of additive codes over \F_{4} are used in the construction of many asymmetric quantum codes over \F_{4}.Comment: Accepted for publication March 2, 2011, IEEE Transactions on Information Theory, to appea

Low Correlation Sequences over the QAM Constellation

This paper presents the first concerted look at low correlation sequence families over QAM constellations of size M^2=4^m and their potential applicability as spreading sequences in a CDMA setting. Five constructions are presented, and it is shown how such sequence families have the ability to transport a larger amount of data as well as enable variable-rate signalling on the reverse link. Canonical family CQ has period N, normalized maximum-correlation parameter theta_max bounded above by A sqrt(N), where 'A' ranges from 1.8 in the 16-QAM case to 3.0 for large M. In a CDMA setting, each user is enabled to transfer 2m bits of data per period of the spreading sequence which can be increased to 3m bits of data by halving the size of the sequence family. The technique used to construct CQ is easily extended to produce larger sequence families and an example is provided. Selected family SQ has a lower value of theta_max but permits only (m+1)-bit data modulation. The interleaved 16-QAM sequence family IQ has theta_max <= sqrt(2) sqrt(N) and supports 3-bit data modulation. The remaining two families are over a quadrature-PAM (Q-PAM) subset of size 2M of the M^2-QAM constellation. Family P has a lower value of theta_max in comparison with Family SQ, while still permitting (m+1)-bit data modulation. Interleaved family IP, over the 8-ary Q-PAM constellation, permits 3-bit data modulation and interestingly, achieves the Welch lower bound on theta_max.Comment: 21 pages, 3 figures. To appear in IEEE Transactions on Information Theory in February 200

First evidence of cryptotephra in palaeoenvironmental records associated with Norse occupation sites in Greenland

The Norse/Viking occupation of Greenland is part of a dispersal of communities across the North Atlantic coincident with the supposed Medieval Warm Period of the late 1st millennium AD. The abandonment of the Greenland settlements has been linked to climatic deterioration in the Little Ice Age as well as other possible explanations. There are significant dating uncertainties over the time of European abandonment of Greenland and the potential influence of climatic deterioration. Dating issues largely revolve around radiocarbon chronologies for Norse settlements and associated mire sequences close to settlement sites. Here we show the potential for moving this situation forward by a combination of palynological, radiocarbon and cryptotephra analyses of environmental records close to three ‘iconic’ Norse sites in the former Eastern Settlement of Greenland – Herjolfsnes, Hvalsey and Garðar (the modern Igaliku). While much work remains to be undertaken, our results show that palynological evidence can provide a useful marker for both the onset and end of Norse occupation in the region, while the radiocarbon chronologies for these sequences remain difficult. Significantly, we here demonstrate the potential for cryptotephra to become a useful tool in resolving the chronology of Norse occupation, when coupled with palynology. For the first time, we show that cryptotephra are present within palaeoenvironmental sequences located within or close to Norse settlement ruin-groups, with tephra horizons detected at all three sites. While shard concentrations were small at Herjolfsnes, concentrations sufficient for geochemical analyses were detected at Igaliku and Hvalsey. WDS-EPMA analyses of these tephra indicate that, unlike the predominantly Icelandic tephra sources reported in the Greenland ice core records, the tephra associated with the Norse sites correlate more closely with volcanic centres in the Aleutians and Cascades. Recent investigations of cryptotephra dispersal from North American centres, along with our new findings, point to the potential for cryptotephra to facilitate hypothesis testing, providing a key chronological tool for refining the timing of Norse activities in Greenland (e.g. abandonment) and of environmental contexts and drivers (e.g. climate forcing)

Evolutionary history and identification of conservation units in the giant otter, Pteronura brasiliensis.

The giant otter, Pteronura brasiliensis, occupies a range including the major drainage basins of South America, yet the degree of structure that exists within and among populations inhabiting these drainages is unknown. We sequenced portions of the mitochondrial DNA (mtDNA) cytochrome b (612 bp) and control region (383 bp) genes in order to determine patterns of genetic variation within the species. We found high levels of mtDNA haplotype diversity (h = 0.93 overall) and support for subdivision into four distinct groups of populations, representing important centers of genetic diversity and useful units for prioritizing conservation within the giant otter. We tested these results against the predictions of three hypotheses of Amazonian diversification (Pleistocene Refugia, Paleogeography, and Hydrogeology). While the phylogeographic pattern conformed to the predictions of the Refugia Hypothesis, molecular dating using a relaxed clock revealed the phylogroups diverged from one another between 1.69 and 0.84 Ma, ruling out the influence of Late Pleistocene glacial refugia. However, the role of Plio-Pleistocene climate change could not be rejected. While the molecular dating also makes the influence of geological arches according to the Paleogeography Hypothesis extremely unlikely, the recent Pliocene formation of the Fitzcarrald Arch and its effect of subsequently altering drainage pattern could not be rejected. The data presented here support the interactions of both climatic and hydrological changes resulting from geological activity in the Plio-Pleistocene, in shaping the phylogeographic structure of the giant otter