A reference or a source of this information would really help.
3-Weight Method
The 3-Weight Methods is also known as the Electronic Funds Transfer Routing Number Scheme used by the banking industry. It is a mod 10 based system, but rather than operating on n as a whole number, it operates on a dot product (i.e., the individual digits of the number n).
So, given an 8 digit routing number, the check digit c = n · (7, 3, 9, 7, 3, 9, 7, 3), mod 10. Stated another way, let ai be the ith digit of n (most significant to least significant). Then
c = 7a1 + 3a2 + 9a3 + 7a4 + 3a5 + 9a6 + 7a7 + 3a8 mod 10
c is then concatenated to the 8 digit route, forming a 9 digit routing number
This scheme is based on the fact that multiplication modulo 10 yields a permutation of the 10 decimal digits if the multiplication factor is a digit of the set { 1, 3, 7, 9 }; but only a subset of the decimal digits if the factor is 5 or an even digit. This system cannot detect adjacent transpositions of digits that differ by 5.
The 3-Weight method does not use simple modular reductions, so c = 10 - c is not needed to hold the equality.
The reader should find the following check equation holds true (where a9 is -c):
0 = 7a1 + 3a2 + 9a3 + 7a4 + 3a5 + 9a6 + 7a7 + 3a8 + a9 mod 10
The 3-Weight Scheme is presented below. As the reader can see, it generalizes to a arbitrary length of digits easily. However, if the reader desires a system for very long datasets, or binary data sets consider using a CRC or Alder checksums, or a hash-based checksum.
What I have tried:
yes
I have tried but I have not been successful in obtaining the source of this information apart from this website. Has the 3 - weight method been studied before? Kindly point me in the right direction so that I can read more about it.
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