A note on minor errors in the
International QR Barcode standard
ISO/IEC 18004:2000(E)
Johan Persson
Aditus Consulting, Sweden
25 August 2008
email: johanp@aditus.nu
Abstract
In this note we describe why the encoding example shown in Annex G of
the QR barcode international standard [1] has chosen an incorrect XOR mask
in the final step of the encodation process.
Annex G in the standard uses the optical XOR mask identified by index
3 (011) but we claim that the mask with index 7 (111) gives an overall lower
penalty score according to the rules set out in the standard in section 8.8.1. This
note details and motivates our claim.
We also point out one further minor error and one omission in the
standard in the two concluding appendices to this note.
(15 pages)
1 Introduction
In the final step of the creation of the matrix representing the 2-dimensional QR barcode the standard
specifies that a suitable XOR mask should be applied to the matrix representing the QR barcode in order to
secure good optical conditions for the barcode reader/scanner.
It should be noted that the selection of this mask (which is applied to the bit matrix with a XOR
operation) is somewhat arbitrary. The purpose of this XOR mask at the end of the encoding process is to
make the overall distribution of black and white areas as even as possible given the encoded data. This will
then serve to reduce the risk for faulty readings by scanners by maximizing the optical information in the
matrix (achieving high frequency content). The QR standard specifies that 8 different masks (defined in
section 8.8.1 in the standard) should be considered.
Since the information about what mask is chosen is encoded in the barcode unaffected by the chosen
mask, (since it is part of the functional patterns which are excluded from the mask operation), a QR reader
will always have information on what mask has been chosen and can therefore retrieve the original bit
pattern. Hence, the actual selection of the mask is not absolutely critical since several masks can give similar
optical performance. The standard specifies a method to evaluate each mask in turn by calculating a penalty
score. The mask with the lowest penalty score should then be chosen.
In the following discussion we will assume that the reader has basic technical knowledge of the
structure of the QR code and is familiar with the encodation procedure. The discussion will be restricted to
comparing the final application of the mask once the encodation of data and bit placement in the matrix has
been done according to the rules of the QR barcode.
The data used in this note is the same as is used in Annex G, a string consisting of 8 numeric values,
”01234567”, encoded using numerical encodation schema and QR version 1-M for the layout and error
correction level.
2 Applying mask 3 and 7 to the original bit placement
The result after applying mask with index 3 and 7 to the matrix corresponding to the data '01234567'
(as used in Annex G in [1]) is shown in Figure 1 ('-' corresponds to a binary 0 and 'X' corresponds to a binary
1 in the textual representation of the matrix). For easier visual reference to the individual modules in the
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