The Hardness of Code Equivalence over Fq\mathbf{F}_q and its Application to Code-based Cryptography

International audienceThe code equivalence problem is to decide whether two linear codes over F_q are equivalent, that is identical up to a linear isometry of the Hamming space. In this paper, we review the hardness of code equivalence over F_q due to some recent negative results and argue on the possible implications in code-based cryptography. In particular, we present an improved version of the three-pass identification scheme of Girault and discuss on a connection between code equivalence and the hidden subgroup problem

Shearwater Foraging in the Southern Ocean: The Roles of Prey Availability and Winds

Background Sooty (Puffinus griseus) and short-tailed (P. tenuirostris) shearwaters are abundant seabirds that range widely across global oceans. Understanding the foraging ecology of these species in the Southern Ocean is important for monitoring and ecosystem conservation and management. Methodology/Principal Findings Tracking data from sooty and short-tailed shearwaters from three regions of New Zealand and Australia were combined with at-sea observations of shearwaters in the Southern Ocean, physical oceanography, near-surface copepod distributions, pelagic trawl data, and synoptic near-surface winds. Shearwaters from all three regions foraged in the Polar Front zone, and showed particular overlap in the region around 140°E. Short-tailed shearwaters from South Australia also foraged in Antarctic waters south of the Polar Front. The spatial distribution of shearwater foraging effort in the Polar Front zone was matched by patterns in large-scale upwelling, primary production, and abundances of copepods and myctophid fish. Oceanic winds were found to be broad determinants of foraging distribution, and of the flight paths taken by the birds on long foraging trips to Antarctic waters. Conclusions/Significance The shearwaters displayed foraging site fidelity and overlap of foraging habitat between species and populations that may enhance their utility as indicators of Southern Ocean ecosystems. The results highlight the importance of upwellings due to interactions of the Antarctic Circumpolar Current with large-scale bottom topography, and the corresponding localised increases in the productivity of the Polar Front ecosystem

The complexity of counting edge colorings and a dichotomy for some higher domain Holant problems

We show that an effective version of Siegel’s Theorem on finiteness of integer solutions and an application of elementary Galois theory are key ingredients in a complexity classification of some Holant problems. These Holant problems, denoted by Holant(f), are defined by a symmetric ternary function f that is invariant under any permutation of the κ ≥ 3 domain elements. We prove that Holant(f) exhibits a complexity dichotomy. This dichotomy holds even when restricted to planar graphs. A special case of this result is that counting edge κ-colorings is #P-hard over planar 3-regular graphs for κ ≥ 3. In fact, we prove that counting edge κ-colorings is #P-hard over planar r-regular graphs for all κ ≥ r ≥ 3. The problem is polynomial-time computable in all other parameter settings. The proof of the dichotomy theorem for Holant(f) depends on the fact that a specific polynomial p(x, y) has an explicitly listed finite set of integer solutions, and the determination of the Galois groups of some specific polynomials. In the process, we also encounter the Tutte polynomial, medial graphs, Eulerian partitions, Puiseux series, and a certain lattice condition on the (logarithm of) the roots of polynomials.

Urge to cough and its application to the behavioural treatment of cough

The Urge-To-Cough has recently been recognised as a significant factor in understanding the pathophysiology of cough. The principles in the urge to cough model are relevant to the behavioural management of laryngeal conditions including chronic non-specific cough, cough due to paradoxical vocal fold movement, aspiration and reflux. This paper analyses the pathophysiology and behavioural management of these conditions according to the urge to cough model

An algorithm for computing the minimum distances of extensions of BCH codes embedded in semigroup rings

An algorithm is given for computing the weights of extensions of BCH codes embedded in semigroup rings as ideals. The algorithm relies on a more general technical result of independent interest

Inflight Icing Data, A Comparison of Tasmania and British Isles/Central France Air Operations Icing Encounters

Peer reviewed: YesNRC publication: Ye