🚀 go-pugleaf

Howdy!

Someone recently brought me a problem concerning an error-detecting weighted
code with a modulo 11 checksum that she's using in her business. 

In short, a bunch of items are given 10 digit identification numbers. 
Let N_i denote the ith digit of the number.
Each number has the property that SUM(A_i * N_i) is congruent to 0 mod 11,
where {A_i} are weights as follows: {1, 2, 5, 3, 6, 4, 8, 7, 10, 9}.

The obvious advantages of this identification system are that no single
digit errors in a valid number and no single transposition of digits in
a valid number will produce another valid number. 

Question: What is the advantage of the weights being mixed up like that?
(i.e. why isn't A_i just set equal to i?)
References about this particular system would be the most appreciated because 
I know this weighting must have been written about somewhere. I just can't
find it.

Thanks,

Richard 
gibson@math.ucb.edu