# Boost-Commit :

Subject: [Boost-commit] svn:boost r72931 - sandbox/SOC/2011/checks/libs/checks/doc
From: pierre.talbot.6114_at_[hidden]
Date: 2011-07-06 17:21:46

Date: 2011-07-06 17:21:44 EDT (Wed, 06 Jul 2011)
New Revision: 72931
URL: http://svn.boost.org/trac/boost/changeset/72931

Log:
Rubbish explanations of the alternated and transposition errors.
Text files modified:
sandbox/SOC/2011/checks/libs/checks/doc/errors.qbk | 21 +++++++++++++++++++++
1 files changed, 21 insertions(+), 0 deletions(-)

Modified: sandbox/SOC/2011/checks/libs/checks/doc/errors.qbk
==============================================================================
--- sandbox/SOC/2011/checks/libs/checks/doc/errors.qbk (original)
+++ sandbox/SOC/2011/checks/libs/checks/doc/errors.qbk 2011-07-06 17:21:44 EDT (Wed, 06 Jul 2011)
@@ -1,14 +1,35 @@
[section:errors Type of errors]
+
The following sections will describe some of the errors that an user or a device can make.
Those are the most frequent and we are not exhaustive, however we will find out how well our algorithms work.
We will calculate (in a mathematical way) the probability of failures and the factors which affect it.

[h4 Alteration]
+
[h5 Single error]
+
+If the digits are added, an alteration of one digit will render the sum different and therefore the check digit.
+
[h5 Multiple error]

+If more than one digit is altered, a simple sum can't ensure that the check digit will be different.
+In fact it depends on the compensation of the altered digits.
+For example : 1 + 2 + 3 = 6. If we alter 2 digits, the sum could become : 2 + 2 + 2 = 6. The result is equal because 1 + 3 = 2 + 2, the digits altered are compensated.
+
[h4 Transposition]

+A transposition on a simple sum is impossible to detect because the addition is commutative, the order is not important.
+A solution is to associate the position of a digit with a weight.
+
+The Luhn algorithm alternates a digit multiply by two and a simple digit. All twin transpositions are catched but the sequence "90" or "09" because:
+
+9*2 = 18 and 18-9 = 9 so 9*2 = 9
+0*2 = 0
+
+The two digits have the same value if there are doubled or not.
+
+[note A transposition is only catched if the two digits transposed have a different weight and their values with or without weight are not the same.]
+
[h4 Length]
[h4 Phonetic error]