Page 177 - ISCI’2017

n
M = ∏ m i .) uniquely determines the corrective possibilities of error-correcting code nonpositional.
i= 1
Correcting codes in SRC can have any value of the minimum code distance (MCD) d min ) . This
(SRC
depends on the values of redundancy R . In SRC established between redundancy correcting code R

, the value d min ) of MCD and the number k of check bases. Correcting code has a value d (SRC ) of
(SRC
min
MCD, if the degree R of redundancy is not less than the product of any d (SRC ) − 1 bases SRC. On
min
the one hand we have that

( SRC
d min ) − 1
R ≥ ∏ m ,
i q
i= 1
on the other hand, on the other hand –

i ∏
R = M 0 / M = ∏ nk+ m i ∏ / n m = k m ni+ .
i= 1 i= 1 i= 1
(SRC
In this case, legitimately argue that d min ) −=
1 k , or
d min ) = k + 1. (1)
(SRC

There are two approaches to the problem of ensuring NCS in SRC necessary corrective properties.

The first approach. Knowing the requirements for correcting the NCS properties, for example, the
number of errors witch detected t det. or corrected t cor . , to introduce, by controlling the amount k or

magnitude {m nk+ } of bases necessary redundancy information R . Information redundancy R

(SRC
determines the minimum code distance d min ) NCS in SRC.

Then, in accordance with the theory of error-correcting coding (TECC) for the orderly (m < m i+ 1 )
i
SRC have that

t det. ≤ d min ) − 1, (2)
(SRC
t det. ≤ k ; (3)

 d (SRC ) − 1
t cor . ≤  min  , (4)
 2 

k 
t cor . ≤  . (5)
2

The second approach. For a given type of NCS A SRC = (a 1 || a 2 ||...|| a i− 1 || aa i+ 1 ||...|| a n ||...|| a n k+ )
||
i
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