Page 182 - ISCI’2017

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II. Diagnostics data A 3360 = (0 ||0 ||0 ||0 ||5). In accordance with the method of projections [1,2],
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we construct possible projections A of the number A 3360 = (0 ||0 ||0 ||0 ||5):
j
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A = (0 ||0 ||0 ||5), A = (0 ||0 ||0 ||5), A = (0 ||0 ||0 ||5), A = (0 ||0 ||0 ||5) и A = (0 ||0 ||0 ||0).
3
2
1
4
5
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The formula for calculating of the projections of values A j PNS in the PNS has the form [1]
 n 
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A j PNS =   ∑ aB ij   mod M = j (a B + 1 j a B + 2 j + a B nj )mod M . (11)
⋅
⋅
⋅
⋅
i
j
1
2
n
 i= 1; 
 j= 1, n+ 1. 
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In accordance with the formula (11) we can calculate all the values A j PNS . Next, we perform
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(n + 1) a comparison of numbers A j PNS with the number M = M 0 / m n+ 1 . If among the projections
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)
A have number no inside information [0, M numerical range (i.e. A ≥ M ), which contains k of
i
k
the correct numbers, than it is concluded that these k residual of the number A are not distorted.
Erroneous may be only the remains which are among the remaining [(n + 1) k residual number
−
]
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A SRC . Set of the partial working base for a given SRC and set of partial orthogonal bases are presented
in [6-9]. So, we have that
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⋅
⋅
⋅
⋅
⋅
A 1PNS =   4 a B 1 i ∑  mod M = 1 (a B + 11 aB + 21 a B + 31 aB 41 )mod M = 1
3
i
1
4
2
 i= 1 
= (0 385 0 616 0 1100 5 980)mod1540⋅ +⋅ +⋅ + ⋅ = 280 < 420 .
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We conclude that the residual a of числа A – it is possibly a distorted residual;
1
1
1
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⋅
A 2PNS =   4 a B 2 i ∑  mod M = 2 (a B + 12 aB + 22 a B + 32 aB 42 )mod M = 2
⋅
⋅
⋅
⋅
2
4
3
i
1
 i= 1 
= (0 385 0 231 0 330 5 210)mod1155 1050⋅ +⋅ +⋅ + ⋅ = > 420.
Thus, we find that a accurate not distorted residual;
2
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⋅
⋅
⋅
⋅
⋅
A =   4 a B 3 i ∑  mod M = 3 (a B + 13 aB + 23 a B + 33 aB 43 )mod M = 3
4
2
3
1
 3PNS i= 1 i 
= (0 616 0 693 0 792 5 672)mod 924 588⋅ +⋅ +⋅ + ⋅ = > 420 .
We find that a accurate not distorted residual;
3
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⋅
⋅
⋅
⋅
A 4PNS =   4 a B 4 i ∑  mod M = 4 (a B + 14 aB + 24 a B + 34 aB 44 )mod M = 4
⋅
4
2
1
i
3
 i= 1 
(0 220 0 165 0 369 5 540)mod660⋅ +⋅ +⋅ + ⋅ = 60 < 420 .
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Conclusion: the residual a to modular m of number A – perhaps distorted residual a
4
4
4
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