编码论和信息论（英文版）

定　价：¥76.00

作　者：	美Steven Roman著
出版社：	世界图书出版公司北京公司
丛编项：	Graduate Texts in Mathematics
标　签：	群与组合编码

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ISBN：	9787506233927	出版时间：	1998-01-01	包装：	胶版纸
开本：	20cm	页数：	486页	字数：

内容简介

　　The main problem of information and coding theory can be described in a simple way as follows. Imagine that a stream of source data， say in the form of bits（0's and 1's）， is being transmitted over a communications channel， such as telephone line. From time to time， disruptions take place along the channel， causing some of the 0's to be turned into 1's， and vice-versa. The question is "How can we tell when the original source data has been changed， and then it has， how can we recover the original data？"本书为英文版。

作者简介

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图书目录

Preface
Introduction
Part1InformationTheory
Chapter1
Entropy
1.1EntropyofaSource
TheEntropyFunctionH(p1,...,pn)
TheUnitsofEntropy
TheEntropyofaRandomVariable;JointEntropy
1.2PropertiesofEntropy
TileRangeoftheEntropyFunction
AGroupingAxiomforEntropy
PropertiesofJointEntropy
TheConvexityoftheEntropyFunction
EntropyasanExpectedValue
1.3AdditionalPropcrtlesofEntropy
TheEntropyofCountablyInfiniteDistributions
TypicalSequences
Chapter2
NoiselessCoding
2.1VariableLengthEncoding
StringsandCodes
AverageCodewordLength
FixedandVariableLengthCodes
UniqueDecipherability
InstantaneousCodes;ThePrefixProperty
Kraft'sTheorem
McMillan'sTheorem
2.2HuffmanEncoding
AnExampleofHuffmanEncoding
MotivationfortheGeneralCase
TheGeneralCase
Huffman'sAlgorithm
2.3TheNoiselessCodingTheorem
ExtensionsofaSource
Chapter3
NoisyCoding
3.1TheDiscreteMemorylessChannelandConditionalEntropy
DiscreteMemorylessChannels
ConditionalEntropy
SomeSpecialChannels
3.2MutualInformationandChannelCapacity
MutualInformation
ASummaryofProperties
TheCapacityofaChannel
3.3TheNoisyCodingTheorem
TheChannel
TheDecisionScheme
TheProbabilityofaDecisionError
TheRateofaCode
TheNoisyCodingTheorem
TheWeakConverseoftheNoisyCodingTheorem
TheStrongConverseoftheNoisyCodingTheorem
3.4ProofoftheNoisyCodingTheoremandItsStrongConverse
MoreontheProbabilityofError
ProofoftheNoisyCodingTheorem
ProofoftheStrongConverse
Part2CodingTheory
Chapter4
GeneralRemarksonCodes
4.1ErrorDetectionandCorrection
BlockCodes
TileChannel
BurstErrors
TheDecisionScheme
ProbabilitiesAssociatedwithErrorDetection
ProbabilitiesAssociatedwithErrorCorrection
TheNoisyCodingTheorem
4.2MinimumDistanceDecoding
MinimumDistanceDecoding
t-Error-Correctingandt-Error-DetectingCodes
UsingaCodeforSimultaneousErrorCorrection/Detection
TileRelationshipBetweenMinimumDistanceandthe
ProbabilityofError
TilePackingandCoveringRadiiofaCode
PerfectandQuasi-PerfectCodes
4.3FamiliesofCodes
SystematicCodes
FiniteFields
EquivalenceofCodes
TypesofCodes
LinearCodes
NonlinearCodes
FamiliesofCodes
RepetitionCodes
HammingCodes
GolayCodes
Reed-MullerCodes
BCHCodesandReed-SolomonCodes
QuadraticResidueCodes
GoppaCodes
JustesenCodes
PerfectCodes
ObtainingNewCodesfromOldCodes
ExtendingaCode
PuncturingaCode
ExpungingaCode
AugmentingaCode
ShorteningaCode
The(u,u+v)-Construction
TheAutomorphismGroupofaCode
*TransitivePermutationGroups
4.4CodesandDesigns
t-Designs
TheIntersectionNumbersofat-Design
DesignsandCodes
4.5TheMainCodingTheoryProblem
Overview
ElementaryResults
ALowerBoundonAq(n,d)
UpperBoundsonAq(n,d)
ElementaryResults
SmallValuesofAq(n,d)
ALowerBoundonAq(n,d)
UpperBoundsonAq(n,d)
TheSingletonBound
TheSphere-PackingBound
*TheNumbersA(n,d,w)
*TheJohnsonBound
ThePlotkinBound
*EqualityinthePlotkinBound-Hadamardcodes
*TheEliasBound
Chapter5
LinearCodes
5.1LinearCodesandTheirDuals
TheGeneratorMatrixofaLinearCode
TheDualofaLinearCode
SyndromeDecoding
TileProbabilityofCorrectDecoding
TheProbabilityofErrorDetection
MajorityLogicDecoding
Self-DualCodes
*TheNumberofBinarySelf-DualCodes
BurstErrorDetectionandCorrection
5.2WeightDistributions
Characters
TheGroupAlgebra
TheTransformofallElementoftheGroupAlgebra
WeightEnumeratorsandWeightDistributions
TheKrawtchoukPolynomials
LinearCodes
MomentsoftheWeightDistribution
DistanceDistributions
TheFourFundamentalParametersofaCode
TileLinearProgrammingBound
5.3MaximumDistanceSeparableCodes
TheTrivialMDSCodes
CharacterizationsofMDSCodes
ExistenceofNontrivialMDSCodes
TheWeightDistributionofallMDSCode
MDSCodesfromVandermondeMatrices
5.4InvariantTheoryandSelf-DualCodes
Introduction
InvariantTheory
TheWeightEnumeratorofaSelf-DualCode
TheWeightEnumeratorofallEvenSelf-DualCode
Chapter6
SomeLinearCodes
6.1HammingandGolayCodes
HammingCodes
DecodingwithaHammingCode
ANonlinearCodewiththeHammingParameters
HammingCodesandDesigns
SimplexCodes
GolayCodes
TileBinaryGolayCode24
DecodingtileBinaryGolayCode24
TheBiaaryGolayCode23
TileTernaryGolayCodes
PerfectCodes
TheNordstrom-RobinsonCode
6.2Recd-MullerCodes
BooleanFunctionsandBooleanPolynomials
BooleanFunctions
BooleanPolynomials
TheVectorSpacesBmandBm
Reed-MullerCodes
TileReed-MullerCodesas(u,u+v)-Constructions
TileDualof(r,m)
EuclideanGcometry
AGeometricLookattheReed-MullerCodes
DecodingtheReed-MullerCodes
Chapter7
FiniteFieldsandCyclicCodes
7.1BasicPropertiesofFiniteFields
ACharacterizationofFiniteFields
TheSubfieldsofaFiniteField
TheMultiplieativeStructureofaFiniteField
DescribingtheElementsofaFiniteField
7.2IrreduciblePolynomialoverFiniteFields
TheSplittingFieldofanIrreduciblePolynomial
TheNatureoftileRootsofanIrreduciblePolynomial
ComputingMinimalPolynomials
TheAutomorphismGroupofFqn
NormalBases
LinearizedPolynomials
TheNumberofIrreduciblePolynomials
7.3TheRootsofUnity
RootsofUnity
PrimitiveFieldElementsandPrimitiveRootsofUnity
AMethodforFactoringXn-1
TheOrderofanIrreduciblePolynomial
ComputingtheOrderofanIrreduciblePolynomial
TheCyelotomicPolynomials
7.4CyclicCodes
TheGeneratorPolynomialofaCyclicCode
TheCheckPolynomialofaCyclicCode
TheZerosofaCyclicCode
HammingCodesasCyclicCodes
TheldempotentGeneratorofaCyclicCode
MinimalCyclicCodes
FindingGeneratingIdempotents
AFormulaforPrimitiveIdempotents
7.5MoreonCyclicCodes
Mattson-SolomonPolynomials
EncodingwithaCyclicCode
ANonsystematicMethod
ASystematicMethod
DecodingwithaCyclicCode
ErrorTrapping
BurstErrorDetectionandCorrectionwithCyclicCodes
Interleaving
Chapter8
SomeCyclicCodes
8.1BCIICodes
TheBCHBound
BCHCodes
BinaryBCHCodes
TheAutomorphismsofBinaryBCHCodes
TheTrueMinimumDistanceofaBCHCode
TheQualityofBCHCodes
Double-Error-CorrectingBCHCodes
DecodingBCtlCodes
NoErrors
ExactlyOneError
ExactlyTwoErrors
TheGeneralCase
8.2Reed-SolomonandJustesenCodes
Reed-SolomonCodes
PropertiesoftheReed-SolomonCodes
TheReed-SolomonCodesareMDSCodes
TheDualofaReed-SolomonCode
ExtendingaReed-SolomonCode
ObtainingaBinaryCodefroma2m-aryCode
BurstErrorCorrection
ldempotentsofReed-SolomonCodes
EncodingReed-SolomonCodes
DecodingReed-SolomonCodes
AsymptoticallyGoodCodes
FindingGoodFamiliesofCodes
ConcatenationofCodes
JustesenCodes
AnAsymptoticallyGoodFamilyofJustesenCodes
8.3AlternantCodesandGoppaCodes
AlternantCodes
GoppaCodes
TheParametersofF(G,L)
BinaryGoppaCodes
FastDecodingofAlternantCodes
TheEuclideanAlgorithm
DecodingofAlternantCodes-TheInitialSetup
DecodingofAlternantCodes-TheDecodingStep
8.4QuadraticResidueCodes
QuadraticResidues
QuadraticResidueCodes
TheGolayCodesasQuadraticResidueCodes
TheSquareRootBound
TheIdempotentsofaBinaryQuadraticResidueCode
DualsoftheQuadraticResidueCodes
TheExtendedQuadraticResidueCodes
Appendix
Preliminaries
A.1AlgebraicPreliminaries
Groups
Euler'sFormula
CyclicGroups
RingsandFields
IIomomorphisms
Ideals
FactorRings
TheCharacteristicofaRing
ExtensionFields
ThePrimeField
SimpleExtensions
TheRootsofPolynomials
SplittingFields
Polynomials
TheDivisionAlgorithmanditsConsequences
TheEuclideanAlgorithm
IrreduciblePolynomials
CommonRoots
TheMinimalPolynomial
MultipleRoots
A.2MobiusInversion
PartiallyOrderedSets
TheIncidenceAlgebraofaPartiallyOrderedSet
ClassicalMSbiusInversion
MultiplicativeVersionofMSbiusInversion
A.3BinomialInequalities
InequalitiesInvolvingaSingleBinomialCoefficient
InequalitiesInvolvingSumsofBinomialCoefficients
BoundsontheVolumeofaSphere
A.4MoreonFiniteFields
ComputingMinimalPolynomials
AnAlgorithmforFactoringPolynomials
FindingPrimitivePolynomials
Tables
MonicIrreduciblePolynomials
PrimitivePolynomials
FiniteFieldTables
Factorizationofxn-1
KrawtchoukPolynomials
References
SymbolIndex
Index