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The(see 3.1.4.2. Component features - Identifiers) includes a check-digit, which is generated using Verhoeff's dihedral check. This section explains the algorithm used and includes sample source code for generating and checking the check-digit in Java Script and Microsoft Visual Basic.
Verhoeff's Dihedral Group D5 Check
The mathematical description of this technique may appear complex but in practice it can be reduced to a pair of two-dimensional arrays, a single dimensional inverse array and a simple computational procedure. These three arrays are shown in the following tables.
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Position is the position that the digit will have when the has been appended.
The final value of Check is applied to the Inverse D5 array to find the correct.
= ArrayInverseD5 ( Check ).
Sample Java Script for computing Verhoeff's Dihedral Check
The script is presented here as part of an HTML page. The code below can be used by copying all the lines in the above section into an HTML file and opening this with a web browser.
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<!DOCTYPE html SYSTEM "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html>
<head>
<title>SNOMED CT Identifier Check</title>
<style>
body{font-family:Arial, Helvetica, sans-serif}
}
</style>
<meta content="text/html; charset=iso-8859-1" http-equiv="Content-Type"><meta>
<script type="text/javascript" language="JavaScript">
var FnF = new Array();
FnF[0] = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9];
FnF[1] = [1, 5, 7, 6, 2, 8, 3, 0, 9, 4];
for ( var i = 2; i < 8; i++ )
{
FnF[i] = [,,,,,,,,,];
for ( var j = 0; j < 10; j++ )
FnF[i][j] = FnF[i - 1][FnF[1][j]];
}
var Dihedral = new Array(
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[1, 2, 3, 4, 0, 6, 7, 8, 9, 5],
[2, 3, 4, 0, 1, 7, 8, 9, 5, 6],
[3, 4, 0, 1, 2, 8, 9, 5, 6, 7],
[4, 0, 1, 2, 3, 9, 5, 6, 7, 8],
[5, 9, 8, 7, 6, 0, 4, 3, 2, 1],
[6, 5, 9, 8, 7, 1, 0, 4, 3, 2],
[7, 6, 5, 9, 8, 2, 1, 0, 4, 3],
[8, 7, 6, 5, 9, 3, 2, 1, 0, 4],
[9, 8, 7, 6, 5, 4, 3, 2, 1, 0] );
var InverseD5 = new Array(0, 4, 3, 2, 1, 5, 6, 7, 8, 9 );
function VerhoeffCheck()
{
var check = 0;
var IdValue = document.form.numcd.value;
document.getElementById("out").innerText = "";
document.getElementById("out").setAttribute("style", " :red;");
document.getElementById("component").innerText ="Invalid partition";
document.getElementById("component").setAttribute("style", " :green;");
document.getElementById("extnamespace").innerText ="No namespace";
document.getElementById("extnamespace").setAttribute("style", " :red;");
for ( var i=IdValue.length-1; i >=0; i-- )
check = Dihedral[check][FnF[(IdValue.length-i-1) % 8][IdValue.charAt (i)]];
if ( check != 0 ) { document.getElementById("out").innerText = "Check-digit ERROR"; }
else if (IdValue.length < 6) {document.getElementById("out").innerText = "SCTID too short";}
else if (IdValue.length > 18) {document.getElementById("out").innerText = "SCTID too long";}
else {document.getElementById("out").innerText = "Check-digit OK";
document.getElementById("out").setAttribute("style", " :green;");
switch (IdValue.substr(IdValue.length-3,2))
{
case "00":
document.getElementById("component").innerText ="Concept";
document.getElementById("extnamespace").innerText ="International";
break;
case "01":
document.getElementById("component").innerText ="Description";
document.getElementById("extnamespace").innerText ="International";
break;
case "02":
document.getElementById("component").innerText ="Relationship";
document.getElementById("extnamespace").innerText ="International";
break;
case "03":
document.getElementById("component").innerText ="Subset (RF1)";
document.getElementById("extnamespace").innerText ="International";
break;
case "04":
document.getElementById("component").innerText ="Cross Map Set (RF1)";
document.getElementById("extnamespace").innerText ="International";
break;
case "05":
document.getElementById("component").innerText ="Cross Map Target (RF1)";
document.getElementById("extnamespace").innerText ="International";
break;
case "10":
document.getElementById("component").innerText ="Concept";
document.getElementById("extnamespace").innerText =IdValue.substr(IdValue.length-10,7);
break;
case "11":
document.getElementById("component").innerText ="Description";
document.getElementById("extnamespace").innerText =IdValue.substr(IdValue.length-10,7);
break;
case "12":
document.getElementById("component").innerText ="Relationship";
document.getElementById("extnamespace").innerText =IdValue.substr(IdValue.length-10,7);
break;
case "13":
document.getElementById("component").innerText ="Subset (RF1)";
document.getElementById("extnamespace").innerText =IdValue.substr(IdValue.length-10,7);
break;
case "14":
document.getElementById("component").innerText ="Cross Map Set (RF1)";
document.getElementById("extnamespace").innerText =IdValue.substr(IdValue.length-10,7);
break;
case "15":
document.getElementById("component").innerText ="Cross Map Target (RF1)";
document.getElementById("extnamespace").innerText =IdValue.substr(IdValue.length-10,7);
break;
default:
document.getElementById("component").setAttribute("style", " :red;");
}
if (document.getElementById("extnamespace").innerText=='International') {document.getElementById("extnamespace").setAttribute("style", " :green;");}
else if (IdValue.length>10) {document.getElementById("extnamespace").setAttribute("style", " :green;");}
else {document.getElementById("extnamespace").innerText="Invalid Namespace";
}
}
}
function VerhoeffCompute( )
{
var IdValue = document.form.num.value; var check = 0;
document.form.numcd.value= "";
for ( var i = IdValue.length-1; i >=0; i-- )
check = Dihedral[check][FnF[(IdValue.length-i) % 8][IdValue.charAt (i)]];
document.form.numcd.value = document.form.num.value + InverseD5[check];
VerhoeffCheck();
document.getElementById("out").innerText = "Computed check-digit";
}
</script>
</head>
<body>
<h1>SNOMED CT Identifier Check</h1>
<form action="" name="form">
<table border="1" width="441">
<tr>
<td width="212" height="25">
Partial Identifier <br/>(without check-digit)
</td>
<td width="115" height="25">
<input name="num" size="18"/>
</td>
<td width="92" height="25">
<input onclick= "VerhoeffCompute()" type="button" value="Compute"/>
</td>
</tr>
<tr>
<td width="212" height="35">
SNOMED CT Identifier
</td>
<td width="115" height="35">
<input name="numcd" size="18"/>
</td>
<td width="92" height="35">
<input onclick= "VerhoeffCheck()" type="button" value="Check"/>
</td>
</tr>
<tr>
<td width="212" height="23">
Result of check
</td>
<td width="115" height="23" colspan="2" id="out">
</td> </tr>
<tr>
<td width="212" height="23">
Component type
</td>
<td width="115" height="23" colspan="2" id="component">
</td> </tr>
<tr>
<td width="212" height="23">
Namespace
</td>
<td width="115" height="23" colspan="2" id="extnamespace">
</td> </tr>
</table>
<p style="margin-left: 0; margin-right: 0">
This Verhoeff checking part of this code was based on a webpage at:
</p>
<ul>
<li>
<a href="http://www.augustana.ab.ca/~mohrj/algorithms/checkdigit.html">
http://www.augustana.ab.ca/~mohrj/algorithms/checkdigit.html
</a>
</li>
</ul>
</form>
</body>
</html> |
Sample Visual Basic for computing Verhoeff's Dihedral Check
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Option Explicit
Private Dihedral(9) As Variant
Private FnF(7) As Variant
Private InverseD5 As Variant
Public Function VerhoeffCheck(ByVal IdValue As String) As Boolean
'Check the supplied value and return true or false
Dim tCheck As Integer, i As Integer
VerhoeffArrayInit
For i = Len(IdValue) To 1 Step -1
tCheck = Dihedral(tCheck)(FnF((Len(IdValue) - i) Mod 8)(Val(Mid(IdValue, i, 1))))
Next
VerhoeffCheck = tCheck = 0
End Function
Public Function VerhoeffCompute(ByVal IdValue As String) As String
'Compute the check digit and return the identifier complete with check-digit
Dim tCheck As Integer, i As Integer
VerhoeffArrayInit
For i = Len(IdValue) To 1 Step -1
tCheck = Dihedral(tCheck)(FnF((Len(IdValue) - i + 1) Mod 8)(Val(Mid(IdValue, i, 1))))
Next
VerhoeffCompute = IdValue & InverseD5(tCheck)
End Function
Private Sub VerhoeffArrayInit()
'Create the arrays required
Dim i As Integer, j As Integer
'if already created exit here
If VarType(InverseD5) >= vbArray Then Exit Sub
'create the DihedralD5 array
Dihedral(0) = Array(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
Dihedral(1) = Array(1, 2, 3, 4, 0, 6, 7, 8, 9, 5)
Dihedral(2) = Array(2, 3, 4, 0, 1, 7, 8, 9, 5, 6)
Dihedral(3) = Array(3, 4, 0, 1, 2, 8, 9, 5, 6, 7)
Dihedral(4) = Array(4, 0, 1, 2, 3, 9, 5, 6, 7, 8)
Dihedral(5) = Array(5, 9, 8, 7, 6, 0, 4, 3, 2, 1)
Dihedral(6) = Array(6, 5, 9, 8, 7, 1, 0, 4, 3, 2)
Dihedral(7) = Array(7, 6, 5, 9, 8, 2, 1, 0, 4, 3)
Dihedral(8) = Array(8, 7, 6, 5, 9, 3, 2, 1, 0, 4)
Dihedral(9) = Array(9, 8, 7, 6, 5, 4, 3, 2, 1, 0)
'create the FunctionF array
FnF(0) = Array(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
FnF(1) = Array(1, 5, 7, 6, 2, 8, 3, 0, 9, 4)
'compute the rest of the FunctionF array
For i = 2 To 7
FnF (i) = Array(0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
For j = 0 To 9
FnF (i)(j) = FnF(i - 1)(FnF(1)(j))
Next
Next
'Create the InverseD5 array
InverseD5 = Array("0", "4", "3", "2", "1", "5", "6", "7", "8", "9")
End Sub |
Reasons for using a check-digit
Although a user should rarely type the, experience suggests that from time to time this will happen. A user may also copy and paste an. There is a significant risk of errors in these processes and inclusion of ais intended to reduce the risk of such errors passing undetected. The choice ofalgorithm has been made to maximize the detection of common typographical errors. These have been analyzed by in a paper by J. Verhoeff ("Error Detecting Decimal Codes", Mathematical Center Tract 29, The Mathematical Center, Amsterdam, 1969) and subsequently cited in Wagner and Putter, ("Error Detecting Decimal Digits", CACM, Vol 32, No. 1, January 1989). These papers give a detailed categorization of the sorts of errors humans make in dealing with decimal numbers, based on a study of 12000 errors:
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In the explanations above, a is not equal to b, but c can be any decimal digit.
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The check-sums used for credit cards (the IBM check) picks up the most common errors but miss some adjacent transpositions and many jump transpositions. Assuming the pattern of errors described above, on average it will miss between 4% and 5% of expected errors.
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The ISBN modulus 11 (used fornumber) picks up more errors than the IBM checksum. Leaving 2% to 3% of errors undetected. However, it generates a check-sum value of 0 to 10 and thus cannot be represented as a singlein about 9% of cases. The ISBN convention is to use "X" to represent thevalue 10 but this is incompatible with an Integer (data type) representation. Thenumber uses this check-sum but regards and number generating a check-sum of 10 as an invalid. This approach could be applied to thebut this would render 9% of possible values unusable in each partition and. This would prevent a simple sequence of values from being allocated as the "item" within each. More significantly the unusable itemwould differ in eachor partition and this would prevent simple transpositions of itembetween partitions and. Partitions could be a useful way of distinguishing developmental and released components and revising the partition and recalculating thewould then be an elegant way to activate these components for a distribution version. It seems unwise to prevent future development and maintenance by using a check-sum that will prevent this.
Verhoeff's Check
Verhoeff's check catches all single errors, all adjacent transpositions, over 95% of twin errors, over 94% of jump transpositions and jump twin errors, and most phonetic errors. Therefore, like modulus 11, the Verhoeff check reduces the undetected error rate to 2% or 3%. Unlike modulus 11, it does this using a single decimaland without limiting the range of valid numbers.
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