Search results for "Linear code"

showing 9 items of 9 documents

Asymptotically good codes from generalized algebraic-geometry codes

2005

We consider generalized algebraic-geometry codes, based on places of the same degree of a fixed algebraic function field over a finite field. In this note, using a method similar to the Justesen's one, we construct a family of such codes which is asymptotically good.

Algebraic function fieldBlock codeDiscrete mathematicsFunction field of an algebraic varietyApplied MathematicsReal algebraic geometryAlgebraic extensionAlgebraic functionLinear codeExpander codeComputer Science ApplicationsMathematics
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On the decomposition of prefix codes

2017

Abstract In this paper we focus on the decomposition of rational and maximal prefix codes. We present an effective procedure that allows us to decide whether such a code is decomposable. In this case, the procedure also produces the factors of some of its decompositions. We also give partial results on the problem of deciding whether a rational maximal prefix code decomposes over a finite prefix code.

Block codePrefix codeGeneral Computer ScienceComputer science0102 computer and information sciences02 engineering and technologyPrefix grammarKraft's inequality01 natural sciencesPrefix codeTheoretical Computer SciencePrefix codes; Finite automata; Composition of codesComposition of codes0202 electrical engineering electronic engineering information engineeringDiscrete mathematicsSelf-synchronizing codeFinite-state machineSettore INF/01 - InformaticaComputer Science (all)Rational languageLinear codePrefixComposition of code010201 computation theory & mathematicsPrefix codes020201 artificial intelligence & image processingFinite automataComputer Science::Formal Languages and Automata Theory
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Design of efficient codes for the AWGN channel based on decomposable binary lattices

1998

This work is concerned with the use of binary decomposable lattice codes over the QAM Gaussian channel. First, we investigate the structure of such class of lattices: we derive consistency conditions for the binary codes appearing in their decomposition and express their nominal coding gain and some bounds for their error coefficient in terms of the parameters of the component codes. Then we describe a general multistage bounded‐distance decoding algorithm with low complexity and we evaluate its performance. Finally, we develop a design example and report the corresponding simulation results; as a reference some comparisons with standard TCM codes are also presented.

Block codeTheoretical computer scienceApplied MathematicsConcatenated error correction codeBinary numberLinear codeCoding gainComputer Science Applicationssymbols.namesakeAdditive white Gaussian noiseComputational Theory and MathematicssymbolsBinary codeElectrical and Electronic EngineeringAlgorithmDecoding methodsMathematics
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New lower bounds for the minimum distance of generalized algebraic geometry codes

2013

Abstract In this paper, we give a new lower bound for generalized algebraic geometry codes with which we are able to construct some new linear codes having better parameters compared with the ones known in the literature. Moreover, we give a relationship between a family of generalized algebraic geometry codes and algebraic geometry codes. Finally, we propose a decoding algorithm for such a family.

Discrete mathematicsAlgebraic cycleBlock codeAlgebraic function field generalized algebraic geometry codes minimum distanceAlgebra and Number TheoryDerived algebraic geometryFunction field of an algebraic varietyAlgebraic surfaceReal algebraic geometryDimension of an algebraic varietySettore MAT/03 - GeometriaLinear codeMathematicsJournal of Pure and Applied Algebra
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MMD codes in a more general sense

2002

Summary form only given. The author deals with the characterisation of maximum minimum distance (MMD) codes in a more general sense, which has been completed in a joint work with Olsson. As in the m=1 case the weight distribution of an MMD code /spl Cscr/ is uniquely determined by its parameters [n,k,d]/sub q/.

Discrete mathematicsCombinatoricsCode (set theory)Minimum distanceWeight distributionSense (electronics)Linear codeMathematics1998 Information Theory Workshop (Cat. No.98EX131)
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On the size of transducers for bidirectional decoding of prefix codes

2012

In a previous paper [L. Giambruno and S. Mantaci, Theoret. Comput. Sci. 411 (2010) 1785–1792] a bideterministic transducer is defined for the bidirectional deciphering of words by the method introduced by Girod [ IEEE Commun. Lett. 3 (1999) 245–247]. Such a method is defined using prefix codes. Moreover a coding method, inspired by the Girod’s one, is introduced, and a transducer that allows both right-to-left and left-to-right decoding by this method is defined. It is proved also that this transducer is minimal. Here we consider the number of states of such a transducer, related to some features of the considered prefix code X . We find some bounds of such a number of states in relation wi…

Discrete mathematicsPrefix codeBlock codeSettore INF/01 - InformaticaGeneral MathematicsConcatenated error correction codeprefix codeList decodingSerial concatenated convolutional codesSequential decodingLinear codeComputer Science ApplicationsPrefixbilateral decodingVariable length codetransducersAlgorithmComputer Science::Formal Languages and Automata TheorySoftwareMathematics
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Steiner systems and configurations of points

2020

AbstractThe aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner SystemS(t, n, v) we associate two ideals, in a suitable polynomial ring, defining a Steiner configuration of points and its Complement. We focus on the latter, studying its homological invariants, such as Hilbert Function and Betti numbers. We also study symbolic and regular powers associated to the ideal defining a Complement of a Steiner configuration of points, finding its Waldschmidt constant, regularity, bounds on its resurgence and asymptotic resurgence. We also compute the parameters of linear codes associated to any Steiner configur…

Linear codes; Monomial ideals; Stanley Reisner rings; Steiner systems; Symbolic powersSteiner systemsBetti numberPolynomial ring0102 computer and information sciencesAlgebraic geometrySymbolic powers01 natural sciencessymbols.namesakeMathematics - Algebraic GeometryLinear codesTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYMonomial idealsComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONFOS: MathematicsMathematics - CombinatoricsIdeal (ring theory)0101 mathematicsCommutative algebraAlgebraic Geometry (math.AG)Complement (set theory)MathematicsDiscrete mathematicsHilbert series and Hilbert polynomialApplied Mathematics010102 general mathematicsStanley Reisner ringsLinear codes Monomial ideals Stanley Reisner rings Steiner systems Symbolic powersComputer Science Applications51E10 13F55 13F20 14G50 94B27Settore MAT/02 - AlgebraSteiner systemSteiner systems Monomial ideals Symbolic powers Stanley Reisner rings Linear codes010201 computation theory & mathematicssymbolsCombinatorics (math.CO)Settore MAT/03 - GeometriaMathematicsofComputing_DISCRETEMATHEMATICS
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Diagonal space time hadamard codes with erasure decoding algorithm

2005

A major challenge in the area of space time (ST) codes is to find codes suitable for efficient decoding, thus overcoming the problem of many existing ST code designs which require maximum-likelihood (ML) decoding. A solution could be to apply single-input single-output (SISO) channel codes and theory over temporal channel fading to the multi-input single-output (MISO) code construction and classical suboptimum decoding methods. For these purposes, an ST code construction which allows the use of efficient decoding algorithms is described. We propose a concatenated code, where the inner code is the diagonal ST Hadamard (D-STH) code with Paley constructions and the outer code is an algebraic b…

Prefix codeBlock codePolynomial codeComputer scienceConcatenationList decodingData_CODINGANDINFORMATIONTHEORYSequential decodingLocally testable codeSystematic codeReed–Solomon error correctionHadamard transformCyclic codeFadingLow-density parity-check codeComputer Science::Information TheorySelf-synchronizing codeHadamard codeConcatenated error correction codeReed–Muller codeSerial concatenated convolutional codesAntenna diversityLinear codeConvolutional codeErasureConstant-weight codeErasure codeAlgorithmDecoding methodsCommunication channelIEEE Wireless Communications and Networking Conference, 2005
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Recursive modeling for completed code generation

2009

Model-Driven Development is promising to software development because it can reduce the complexity and cost of developing large software systems. The basic idea is the use of different kinds of models during the software development process, transformations between them, and automatic code generation at the end of the development. But unlike the structural parts, fully-automated code generation from the behavior parts is still hard, if it works at all, restricted to specific application areas using a domain specific language, DSL.This paper proposes an approach to model the behavior parts of a system and to embed them into the structural models. The underlying idea is recursive refinements …

Theoretical computer scienceSource codeCode reviewbusiness.industryComputer scienceProgramming languagemedia_common.quotation_subjectSoftware developmentStatic program analysiscomputer.software_genreLinear code sequence and jumpSoftware constructionKPI-driven code analysisCode generationbusinesscomputermedia_commonProceedings of the 1st Workshop on Behaviour Modelling in Model-Driven Architecture
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