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McEliece R.J. - Finite Fields for Computer Scientists and Engineers |
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Предметный указатель |
Antilogarithxns 27
Associate 13 17
Autocorrelation function 156 167
Basis, dual 110
Berlekamp's bit serial multiplication circuits 110ff
Berlekamp's polynomial factorization algorithm 84ff
Binomial coefficients 44 146
Binomial theorem 45 52
Blumer, A. 119
Calculus, freshman 57
Characteristic equation, of linear recursion 124
Chevalley - Warning, Theorem of 182
complex numbers 23 24 70 76
Conjugates 46
Correlation, between two sequences 155
Crosscorrelation function 171-172
Crosstalk 170
Cyclotomic cosets 91
Cyclotomic polynomials 76ff
Decimal, repeating 53
Decimation 162
Degree, of an element in a finite field 47
Derivative, formal 57 72
Distribution problems 137ff
Division algorithm 24
Division, synthetic 24 93
Divisor, proper 14
Domain, integral 3
Euclid 3
Euclid's algorithm, could be taught to junior high school students 6
Euclid's algorithm, extended version of 9
Euclid's algorithm, statement of 7
Euclidean domain, defintion of 3
Euclidean domain, examples of 4
Euler Product technique 58
Euler's function, definition of 33
Euler's function, formulas for 65
Fact, a curious 7 12
Factorization, trivial 13 17
Factorization, unique factorization theorem 15
Fibonacci numbers 7 11 123-125 131 138 141 142 149
Field with four elements 1
Field with one element 2
Field with p elements 1 22
Field, characteristic of 30
Field, definition of 1
Field, finite, existence of 67
Field, infinite are uninteresting 1
Field, uniqueness of 69
Gauss's algorithm for finding primitive roots 38 52
Gaussian integers 4 10 14 17 28
GCD see "Greatest common divisor"
Generating functions 58
Gold sequences 196 200
Greatest common divisor, computationally clumsy algorithm for finding 16
Greatest common divisor, definition of 4
| Greatest common divisor, expressed as a linear combination of things 5
Hilbert's algorithm for solving 104ff
Initial conditions, for linear recurrence relation 123
Junior high school algorithm for finding gcd's 16
Kloosterman sum 174
Lagrange's theorem 31
Linear recurrences 123ff
Linear recurrences, characteristic polynomial 127
Linear recurrences, cycles in equivalent solutions to 134
Linear recurrences, cyclic equivalence of solutions to 132
Logarithms 27
m-gram 152
M-sequences 151ff
m-sequences, canonical cyclic shift of 160
m-sequences, crosscorrelation between two, Big Theorem about 193
m-sequences, cycle-and-add property of 159
m-sequences, number of different 161
m-sequences, run-distribution properties of |
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