Adámek J. — Foundations of Coding :: Электронная библиотека попечительского совета мехмата МГУ

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Adámek J. — Foundations of Coding

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Название: Foundations of Coding

Автор: Adámek J.

Аннотация:

Although devoted to constructions of good codes for error control, secrecy or data compression, the emphasis is on the first direction. Introduces a number of important classes of error-detecting and error-correcting codes as well as their decoding methods. Background material on modern algebra is presented where required. The role of error-correcting codes in modern cryptography is treated as are data compression and other topics related to information theory. The definition-theorem proof style used in mathematics texts is employed through the book but formalism is avoided wherever possible.

Язык:

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 336

Добавлена в каталог: 16.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$d_{free}$       281
$L^{\perp}$       108
$L_{min}$       18
$P_{err}$       45
$P_{und}$       75
$Z_{p}$       80
$\equiv (mod p)$       84 205
$\mathbf{I}$       107
$\mathcal{R}$       137
$\mathfrak{g}$       116
$\mathfrak{R}$       80
$\mathfrak{Z}$       80
Active path      286
Adder      167
Addition modulo 2      63
Algebraic extension      203
Asymptoticaly good codes      254
Augumentation      127
Autoregulation      301
Average length      18
Basis      98
BCH code      239
Binary adder      72
Binary operation      79
Binary symmetric channel      40
Binomial coefficients      223
Binomial theorem      223
Bit      29
Block code      43
Boolean function      138
Boolean polynomial      141
Burst-error      180 245
Capacity      54
Channel      40 50
Characteristic      211
Characteristic function      150 152
Check bit      43
Check symbol      39
Code      6
Code alphabet      5
Code frame      280
Code word      6 279
Code, 2-out-of-5      5
Code, ASCII      9
Code, BCH      239
Code, block      7
Code, burst-error-correcting      189 245
Code, convolutional      271
Code, cyclic      161
Code, dual      120
Code, even-parity      43
Code, expurgated      125
Code, extended      125
Code, Fire      189
Code, generalized Reed – Muller      246
Code, Golay      184 185
Code, Goppa      248 303
Code, Hamming      69 134 230
Code, hexadecimal      9
Code, instantaneous      7
Code, irreducible Goppa      252
Code, ISBN      11
Code, linear      66 115
Code, Morse      7
Code, nontrivial      43
Code, octal      8
Code, perfect      74 183
Code, punctured      127
Code, Reed – Muller      24
Code, Reed – Solomon      245
Code, Simplex      121 297
Code, systematic      117
Code, trivial      43
Code, uniquely decodable      7
Coding      5
Coding of source messages      6
Coherence      27
Commutative group      79
Conditional entropy      53
Congruent modulo      84 93
Consecutive positions      181
Constraint length      277
Continuity      27
Convolutional code      271
Correct burst errors      186
Correct errors      49 279
Coset      81
Coset leader      83 123
Coset modulo p      93
Cryptography      29
Cyclic code      161
D      48
Data Encryption Standard      309
decryption      293
Degree      141 162
Derivative      224
Detect burst errors      185
Detect errors      48
DIMENSION      98
Discrepancy      286
Division of polynomial      163
Dual code      121
e      66
Effectivity      37
Elementary row operation      102
Encoding      72
Encryption      293
entropy      29
Equivalent codes      118
Error evaluation      258
Error location      258
Error pattern      66 121
Error probability      40
error trapping      181
Euclidean algorithm      260
Euclidean geometry      148 151
Euler function      217
Euler – Fermat Theorem      218
Even-parity code      43
Expurgation      127
Extension      125
Extension of a source      32
Fermat's theorem      210
Field      91
Finite-dimensional      98
Fire code      198
Flat      150 151
Free distance      279

G(x)      165
Galois field      206
Generalized Reed – Muller code      245
Generating polynomial      165 275
Generator matrix      116 271 275
Golay code      184
Goppa code      248 303
Greatest common divisor      261
Group      79
H      29 53
H(X)      172
Hamming code      69 134 230
Hamming distance      46
Hamming weight      66
Hexadecimal code      9
Huffman code      18
Hyperplane      151
i      153
Identity matrix      107
Independence theorem      237
information      26
Information source      17
Information, bit      23
Information, frame      280
Information, rate      43
Inner product      105
Instantaneous      7
Interleaving      187
Inverse      79
Inverse matrix      107
Irreducible Goppa code      252
Irreducible polynomial      198
ISBN      11
Isomorphic      88 219
Key      296
Knapsack problem      307
Kraft's inequality      12
Linear code      115
linear combination      97
Linear space      65
Linear subspace      96
Linearly independent      98
Logarithm      28
MacWilliams identity      130
Matrix      101
Maximum-likelihood decoding      48
McMillan's theorem      13
Meggitt decoder      176
Memory      279
Metric      46
Minimal polynomial      213
Minimum distance      48
Minimum weight      66
Monic polynomial      162
Morse code      7
Multiple zero      224
Multiplication modulo2      63
Mutual information      53
Neutral element      79
Octal code      8
Opposite element      79
Order      207
Orthogonal      108
Orthogonal, complement      108
Parity      9
Parity check matrix      68 119
Parity check polynomial      172
Perfect code      74 183
Period      189
Polynomial      162
Polynomial Boolean      141
Positivity      27
Power series      225
Primitive BCH code      240
Primitive element      208
Primitive polynomial      226
Pseudo-random key      297
Public key      303
Puncturing      127
PZ      83
Quotient      163
R      43
Rectangular code      64
Reduced source      19
Redundancy      39
Reed – Muller code      144
Reed – Muller code, generalized      246
Reed – Solomon code      245
Regular matrix      107
Remainder      163
Repetition code      41
Ring      92
Row space      102
Row-echelon form      102
Run      300
S      121
S(X)      175
scalar      95 167
Shannon's fundamental theorem      56
Shannon's Noiseless Coding Theorem      34
Shift-register stage      72 167
Simplex code      121 297
Simultaneous detection and correction      128
Source alphabet      5
span      97
Square matrix      106
Standard array      84
State      281
Subgroup      81
Symmetry      27
Syndrome      72 121 257
Syndrome decoding      123
Syndrome polynomial      175
Systematic      117
TRANSPOSE      106
Trellis diagram      283
Triangle inequality      46
Trivial code      43
Trivial subspace      96
Unique factorization theorem      199
Uniquely decodable      7
Vandermonde matrices      242
Vector      95
Viterbi algorithm      283
Weight enumerator      76
Word      5
Zero      198
Zero word      66

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