Sub-quadratic Decoding of One-point Hermitian Codes

We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realisation of the Guruswami-Sudan algorithm by using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimisation. The second is a Power decoding algorithm: an extension of classical key equation decoding which gives a probabilistic decoding algorithm up to the Sudan radius. We show how the resulting key equations can be solved by the same methods from computer algebra, yielding similar asymptotic complexities.Comment: New version includes simulation results, improves some complexity results, as well as a number of reviewer corrections. 20 page

Decoding of Interleaved Reed-Solomon Codes Using Improved Power Decoding

We propose a new partial decoding algorithm for $m$-interleaved Reed--Solomon (IRS) codes that can decode, with high probability, a random error of relative weight $1-R^{\frac{m}{m+1}}$ at all code rates $R$, in time polynomial in the code length $n$. For $m>2$, this is an asymptotic improvement over the previous state-of-the-art for all rates, and the first improvement for $R>1/3$ in the last $20$ years. The method combines collaborative decoding of IRS codes with power decoding up to the Johnson radius.Comment: 5 pages, accepted at IEEE International Symposium on Information Theory 201

Study case : Utzon et les maisons patios. Une idée et de multiples engagements

En 1953 Jørn Utzon et Ib Møgelvang s’associent pour participer au concours « Private Life », concours d’idée pour un logement bon marché situé en Scanie (NO). Avec leur proposition de maison patio l’équipe remporte le premier prix. Leur proposition est issue des réflexions développées au sein du PAGON et notamment des liens qu’Utzon entretenait avec Sverre Fehn. Elle tient en l’assemblage de cellules d’habitat, la configuration de l’assemblage ancre profondément la valeur de chaque unité par rapport à l’ensemble, et la valeur de l’ensemble par rapport à la nature.Peer Reviewe

Further Generalisations of Twisted Gabidulin Codes

We present a new family of maximum rank distance (MRD) codes. The new class contains codes that are neither equivalent to a generalised Gabidulin nor to a twisted Gabidulin code, the only two known general constructions of linear MRD codes.Comment: 10 pages, accepted at the International Workshop on Coding and Cryptography (WCC) 201

Twisted Reed-Solomon Codes

We present a new general construction of MDS codes over a finite field $\mathbb{F}_q$. We describe two explicit subclasses which contain new MDS codes of length at least $q/2$ for all values of $q \ge 11$. Moreover, we show that most of the new codes are not equivalent to a Reed-Solomon code.Comment: 5 pages, accepted at IEEE International Symposium on Information Theory 201

Improved Power Decoding of One-Point Hermitian Codes

We propose a new partial decoding algorithm for one-point Hermitian codes that can decode up to the same number of errors as the Guruswami--Sudan decoder. Simulations suggest that it has a similar failure probability as the latter one. The algorithm is based on a recent generalization of the power decoding algorithm for Reed--Solomon codes and does not require an expensive root-finding step. In addition, it promises improvements for decoding interleaved Hermitian codes.Comment: 9 pages, submitted to the International Workshop on Coding and Cryptography (WCC) 201

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Grading of parameters for urban tree inventories by city officials, arborists and academics using the Delphi method

Tree inventories are expensive to conduct and update, so every inventory carried out must be maximized. However, increasing the number of constituent parameters increases the cost of performing and updating the inventory, illustrating the need for careful parameter selection. This paper reports the results of a systematic expert rating of tree inventories aiming to quantify the relative importance of each parameter. Using the Delphi method, panels comprising city officials, arborists and academics rated a total of 148 parameters. In order of total mean score, the top ranking parameters, which can serve as a guide for decision-making at practical level and for standardization of tree inventories, were: Scientific name of the tree species and genera, Vitality, Coordinates, Hazard class and Identification number. The study also examined whether the different responsibilities and usage of urban tree databases among organizations and people engaged in urban tree inventories affected their prioritization. The results revealed noticeable dissimilarities in the ranking of parameters between the panels, underlining the need for collaboration between the research community and those commissioning, administrating and conducting inventories. Only by applying such a transdisciplinary approach to parameter selection can urban tree inventories be strengthened and made more relevant