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

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.

Generalized Δ-Y Exchange and k-Regular Matroids

This paper introduces a generalization of the matroid operation of Δ − Y exchange. This new operation, segment-cosegment exchange, replaces a coindependent set of k collinear points in a matroid by an independent set of k points that are collinear in the dual of the resulting matroid. The main theorem of the first half of the paper is that, for every field, or indeed partial field, F, the class of matroids representable over F is closed under segment- cosegment exchanges. It follows that, for all prime powers q, the set of excluded minors for GF(q)-representability has at least 2q−4 members. In the second half of the paper, the operation of segment-cosegment exchange is shown to play a fundamental role in an excluded-minor result for k-regular matroids, where such matroids generalize regular matroids and Whittle's near-regular matroids

Infinite anitchains of matroids with characteristics set {p}

For each prime p, we construct an infinite antichain of matroids in which each matroid has characteristic set fpg. For p = 2, each of the matroids in our antichain is an excluded minor for the class of matroids representable over the rationals

Efficacy of speech pathology management for chronic cough: a randomised placebo controlled trial of treatment efficacy

Background: Chronic cough that persists despite medical treatment may respond to speech pathology intervention, but the efficacy of such treatment has not been investigated in prospective randomised trials. The aim of this study was to determine the efficacy of a speech pathology intervention programme for chronic cough. Methods: A single blind, randomised, placebo controlled trial was conducted in 87 patients with chronic cough that persisted despite medical treatment. Patients were randomly allocated to receive either a specifically designed speech pathology intervention or a placebo intervention. Participants in both groups attended four intervention sessions with a qualified speech pathologist. Results: Participants in the treatment group had a significant reduction in cough (8.9 to 4.6, p, 0.001), breathing (7.9 to 4.7, p < 0.001), voice (7.3 to 4.6, p < 0.001) upper airway (8.9 to 5.9, p < 0.001) symptom scores and limitation (2.3 to 1.6, p < 0.001) ratings following intervention. There was also a significant reduction in breathing (6.8 to 5.6, p=0.047), cough (7.6 to 6.3, p=0.014), and limitation ( 2.3 to 2.0, p=0.038) scores in the placebo group, but the degree of improvement was significantly less than in the treatment group (p < 0.01). Clinical judgement of outcome indicated successful ratings in 88% of participants in the treatment group compared with 14% in the placebo group ( p, 0.001). Conclusion: Speech pathology is an effective management intervention for chronic cough which may be a viable alternative for patients who do not respond to medical treatment

On the Excluded Minors for Quaternary Matroids

AbstractThis paper strengthens the excluded-minor characterization of GF(4)-representable matroids. In particular, it is shown that there are only finitely many 3-connected matroids that are not GF(4)-representable and that have no U2, 6-, U4, 6-, P6-, F−7-, or (F−7)*-minors. Explicitly, these matroids are all minors of S(5, 6, 12) with rank and corank at least 4, and P″8, the matroid that can be obtained from S(5, 6, 12) by deleting two elements, contracting two elements, and then relaxing the only pair of disjoint circuit-hyperplanes

Involuntary glottal closure during inspiration in muscle tension dysphonia

Objective/Hypothesis: The purpose of this study was to examine respiratory function in a group of patients with muscle tension dysphonia (MTD) Design: Cross-sectional analytical study. Methods: Participants included 15 people with a diagnosis of MTD referred to speech pathology for management of their voice disorder, fiberoptic evidence of glottal or supraglottic constriction during phonation with or without posterior chink, or bowing combined and deviation in perceptual voice quality. A second group of 15 participants with no history of voice disorder served as healthy controls,. Baseline pulmonary function test measures included forced expiratory volume in the first second (FEV1), FVC, FEF25 to 75, FIF50, FEV1/FVC, ratio and FEF50/FIF50 ratio. Hypertonic saline challenge test measures included FEV1 and FIF50 after provocation, close response slope, and provocation dose. Results: Compared with healthy controls, participants with MTD demonstrated a higher prevalence of glottal constriction during inspiration after provocation with nebulized hypertonic saline as demonstrated by a reduction in FIF50 after the hypertonic saline challenge. There was no significant difference between the MTD and healthy control groups in baseline pulmonary function testing. Participants with MTD demonstrated a higher prevalence than healthy controls of abnormal glottic closure during inspiration similar to paradoxical vocal fold movement (PVFM). This suggests that they either had previously undiagnosed coexisting PVFM or that the condition of MTD could be expanded to include descriptions of aberrant glottic function during respiration. This study enhances the understanding of PVFM and MTD by combining research advances made in the fields of otolaryngology and respiratory medicine