Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed
Reexamination Certificate
1999-03-16
2002-03-12
Mai, Tan V. (Department: 2121)
Electrical computers: arithmetic processing and calculating
Electrical digital calculating computer
Particular function performed
Reexamination Certificate
active
06356925
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Technical Field
The present invention relates in general to an improved method and system for verifying the accuracy of a numerical sequence. In particular, the present invention relates to a method and system for acquiring a check digit associated with a numeric sequence. More particularly, the present invention relates to an improved check digit method and system that utilize non-commutative matrix multiplication of digits within a numeric sequence to enhance detection of transposition errors.
2. Description of the Related Art
When a sequence of numbers is generated, either by machine or otherwise, and that sequence must later be transcribed and re-entered, transposition errors due to human error or neglect are a significant possibility. In general, transposition errors involve unintentionally “reordering” a particular numeric sequence, such that pairs of digits, or pairs of digit fields, are switched when a given sequence is transcribed or re-entered. An example of a transposition error is illustrated in the following scenario. A numeric sequence “2 3 3 4 6 5”, with corresponding digit places “d
1
d
2
d
3
d
4
d
5
d
6
”, is initially generated. Each digit position may be an information field signifying encoded information, for example. If a person transcribes this sequence from its original display (a computer display screen, for example) onto another medium, he or she may inadvertently switch the numbers in the first two digit positions resulting in an erroneous transcribed sequence of “3 2 3 4 6 5” in which digits “d
1
” and “d
2
” have been transposed.
Check digits are often appended to the end of numeric sequences to enable automatic verification of the accuracy of re-entries of such sequences. There are several known methods for generating and utilizing check digits to identify and verify numeric sequences. Among current check digit methods are “check sum”, “ISBN check”, and “IBM Check”. Although there is some variation among these current check digit methods, they all utilize some form of modulated weighted sum to derive a check digit. Although each of these methods are effective when utilized to detect “misread” errors (those in which a digit within a sequence is simply replaced by an incorrect digit), they are not designed to detect certain transposition errors. As described above, a transposition error involves switching pairs of digits or entire fields within a numeric sequence. Most transposition errors may effectively be detected by current check digit methods. However, check digits which are derived from multiplication and addition computations performed in a space that is commutative (real numbers, for example), permit some transposition errors to pass undetected.
It can therefore be appreciated that a need exists for an improved method and system to produce a check digit that will markedly increase the likelihood of detecting transposition errors that frequently occur upon re-entry of a numeric sequence.
SUMMARY OF THE INVENTION
It is therefore an object of the invention to provide an improved method and system for verifying the accuracy of a numerical sequence.
It is another object of the invention to provide a method and system for acquiring a check digit associated with a numeric sequence.
It is still another object of the invention to provide an improved check digit method and system that utilize non-commutative matrix multiplication of digits within a numeric sequence to enhance detection of transposition errors.
The above and other objects are achieved as is now described. A method and system are disclosed for obtaining a check digit to identify a given numeric sequence of n digits and to verify the accuracy of subsequent entries of the numeric sequence. First, a numeric sequence of n digits is distributed among elements of at least two matrices. Next, the matrices are multiplied together, thereby obtaining a resultant matrix having m elements. Finally, a check digit is derived from the m elements of the resultant matrix, which may be utilized to identify the numeric sequence and verify the accuracy of subsequent entries of the numeric sequence.
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Bracewell & Patterson LLP
International Business Machines - Corporation
Mai Tan V.
Schelkopf J. Bruce
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