On the structure of generalized toric codes

Toric codes are obtained by evaluating rational functions of a nonsingular toric variety at the algebraic torus. One can extend toric codes to the so called generalized toric codes. This extension consists on evaluating elements of an arbitrary polynomial algebra at the algebraic torus instead of a linear combination of monomials whose exponents are rational points of a convex polytope. We study their multicyclic and metric structure, and we use them to express their dual and to estimate their minimum distance

The Common Agricultural Policy and the European Union's Enlargement to Eastern and Central Europe: A Comparison with the Spanish Case

enlargement; Spain; Poland; EU-East-Central Europe; budgetary procedure; treaty reform

NILM techniques for intelligent home energy management and ambient assisted living: a review

The ongoing deployment of smart meters and different commercial devices has made electricity disaggregation feasible in buildings and households, based on a single measure of the current and, sometimes, of the voltage. Energy disaggregation is intended to separate the total power consumption into specific appliance loads, which can be achieved by applying Non-Intrusive Load Monitoring (NILM) techniques with a minimum invasion of privacy. NILM techniques are becoming more and more widespread in recent years, as a consequence of the interest companies and consumers have in efficient energy consumption and management. This work presents a detailed review of NILM methods, focusing particularly on recent proposals and their applications, particularly in the areas of Home Energy Management Systems (HEMS) and Ambient Assisted Living (AAL), where the ability to determine the on/off status of certain devices can provide key information for making further decisions. As well as complementing previous reviews on the NILM field and providing a discussion of the applications of NILM in HEMS and AAL, this paper provides guidelines for future research in these topics.Agência financiadora: Programa Operacional Portugal 2020 and Programa Operacional Regional do Algarve 01/SAICT/2018/39578 Fundação para a Ciência e Tecnologia through IDMEC, under LAETA: SFRH/BSAB/142998/2018 SFRH/BSAB/142997/2018 UID/EMS/50022/2019 Junta de Comunidades de Castilla-La-Mancha, Spain: SBPLY/17/180501/000392 Spanish Ministry of Economy, Industry and Competitiveness (SOC-PLC project): TEC2015-64835-C3-2-R MINECO/FEDERinfo:eu-repo/semantics/publishedVersio

Classical and Quantum Evaluation Codesat the Trace Roots

We introduce a new class of evaluation linear codes by evaluating polynomials at the roots of a suitable trace function. We give conditions for self-orthogonality of these codes and their subfield-subcodes with respect to the Hermitian inner product. They allow us to construct stabilizer quantum codes over several finite fields which substantially improve the codes in the literature. For the binary case, we obtain records at http://codetables.de/. Moreover, we obtain several classical linear codes over the field F 4 which are records at http://codetables.de/

New Quantum Codes from Evaluation and Matrix-Product Codes

Stabilizer codes obtained via CSS code construction and Steane's enlargement of subfield-subcodes and matrix-product codes coming from generalized Reed-Muller, hyperbolic and affine variety codes are studied. Stabilizer codes with good quantum parameters are supplied, in particular, some binary codes of lengths 127 and 128 improve the parameters of the codes in http://www.codetables.de. Moreover, non-binary codes are presented either with parameters better than or equal to the quantum codes obtained from BCH codes by La Guardia or with lengths that can not be reached by them

List decoding of repeated codes

Assuming that we have a soft-decision list decoding algorithm of a linear code, a new hard-decision list decoding algorithm of its repeated code is proposed in this article. Although repeated codes are not used for encoding data, due to their parameters, we show that they have a good performance with this algorithm. We compare, by computer simulations, our algorithm for the repeated code of a Reed-Solomon code against a decoding algorithm of a Reed-Solomon code. Finally, we estimate the decoding capability of the algorithm for Reed-Solomon codes and show that performance is somewhat better than our estimates

Feng-Rao decoding of primary codes

We show that the Feng-Rao bound for dual codes and a similar bound by Andersen and Geil [H.E. Andersen and O. Geil, Evaluation codes from order domain theory, Finite Fields Appl., 14 (2008), pp. 92-123] for primary codes are consequences of each other. This implies that the Feng-Rao decoding algorithm can be applied to decode primary codes up to half their designed minimum distance. The technique applies to any linear code for which information on well-behaving pairs is available. Consequently we are able to decode efficiently a large class of codes for which no non-trivial decoding algorithm was previously known. Among those are important families of multivariate polynomial codes. Matsumoto and Miura in [R. Matsumoto and S. Miura, On the Feng-Rao bound for the L-construction of algebraic geometry codes, IEICE Trans. Fundamentals, E83-A (2000), pp. 926-930] (See also [P. Beelen and T. H{\o}holdt, The decoding of algebraic geometry codes, in Advances in algebraic geometry codes, pp. 49-98]) derived from the Feng-Rao bound a bound for primary one-point algebraic geometric codes and showed how to decode up to what is guaranteed by their bound. The exposition by Matsumoto and Miura requires the use of differentials which was not needed in [Andersen and Geil 2008]. Nevertheless we demonstrate a very strong connection between Matsumoto and Miura's bound and Andersen and Geil's bound when applied to primary one-point algebraic geometric codes.Comment: elsarticle.cls, 23 pages, no figure. Version 3 added citations to the works by I.M. Duursma and R. Pellikaa