In this article, we will talk about two things:
 What does a QR code consist of, and what is the theory behind it?
 General usage of QRCoders.jl and QRDecoders.jl
These packages are created as main works of the OSPP'22 project. They are built following the ISO/IEC 18004:2015 standard, the excellent tutorial and the wikiversityentry. Therefore, images generated by QRCoders.jl can be decoded by a common QR code decoder or by QRDecoders.jl.
For more information, please refer to the announcement in Julia Discourse.
Decomposition of QRCodes
There are two parameters that are crucial to the capacity of a QR code: Version and Error correction level:
 The size of the QR code with version
k(140)
is17+4k x 17+4k
 QR codes have four error correction levels,
L
,M
,Q
,H
. Higher the error correction level needs more error correction bits, thus the capacity of the QR code will be smaller.
The following figure is a QR code with version 7, which is mainly divided into Function Patterns and Encoding Region.

Encoding Region, including format information, version information and encoding data
 Format information is consisted of error correction level and mask pattern, 15 bits in total
 Version information, only exists when version
β₯7
, 18 bits in total  Encoding data: the remaining empty space stores encoding data
Encoding process
The encoding process of QRCodes is a bit complicated, but we can decompose it into several steps:
Choose the best encoding mode from the five modes: Numeric, Alphanumeric, Byte, Kanji and UTF8, and then encode the data into bytes.
Split the message bytes into several small blocks, each block is associated with an error correction block.
Fill in the Function Patterns and Encoding Region.
The Encoding Region is filled from right to left.
Apply different masks to the QR matrix, and pick up the one with lowest penalty score.
Mask patterns are used to make the QR code more scannable. As an example, the following case is designed to confuse the scanner.
Decoding is the reverse process of encoding. The steps are:
 Locate the image
 Read the format area to get the mask pattern
 Apply the mask to restore the original QR matrix
 Extract the encoded data
 Error correction for the encoded data
 Decode the original string from the encoded data
The most difficult parts are locating and errorcorrection.
Theory behind error correction
An example
During data transmission, some errors may occur, such as 1 is transmitted as 0 or some data is lost. Therefore, error correction code is introduced to improve the robustness of the data transmission.
There are three applications of error correction codes: error detection, fill erased data and error correction.
In essence, error correction codes introduce more space to represent a small data set. The redundant information improves the error tolerance of the data. We use an example to illustrate this process.
Suppose Alice wants to send $x\in{0,1}$ to Bob, in order to increase the error tolerance, Alice uses the following encoding scheme
$$
\begin{align*}
x = 0 \quad &\rightarrow &\quad y=000 \
x = 1 \quad &\rightarrow &\quad y=111
\end{align*}
$$
Now Alice sends the encoded $y$ to Bob
 Error correction: suppose at most 1 bit error occurs during transmission, such as $000\rightarrow 010$, obviously Bob can decode $010$ as $0$, thus correct the error
 Error detection: suppose at most 2 bit errors occur during transmission, such as $000\rightarrow 110$, although Bob cannot determine whether the original information is $0$ or $1$, he can determine whether an error occurs during transmission
 fill erased data: suppose 2 bits are lost during transmission, such as $000\rightarrow 0**$, obviously Bob can fill in the missing data to get $000$
Coding Theory
The example above uses a linear code with Hamming distance 3. In general, let $C$ be a linear code with Hamming distance $d$, then
 $C$ can detect at most $e\leq d1$ errors
 $C$ can fill at most $e\leq d1$ erased data
 $C$ can correct at most $e\leq \lfloor\frac{d1}{2}\rfloor$ errors, i.e. $2e\leq d1$
The Hamming distance is the minimum number of bits that need to be changed to convert one code to another, for example, the Hamming distance between $000$ and $010$ is 1, and the Hamming distance between $000$ and $110$ is 2.
Let's understand this theorem through an image. The original information is a set of dots, and we use larger spheres to represent these dots. The Hamming distance of a code is the minimum distance between dots. When the number of errors is within half of the distance, we can always correct them.
ReedSolomon is one of the most commonly used error correction codes. Moreover, it meets the following criterias:
 Stronger error handling ability
 Smaller redundant information as possible
 Efficient encoding and decoding algorithms
General usage

Create a QR code
using QRCoders # creat a QRCode object code = QRCode("Hello World!") # use the object to creat a QR code qrcode(code) # equivalently, use the function directly qrcode("Hello world!")

Export pictures from QR codes
# direct method exportqrcode("Hello world!", "hello.png") # use the object `QRCode` exportqrcode(code)

Export animated GIF from QR codes
exportqrcode(["Hello", "Julia", "!"], "hello.gif")

Specified parameters
code = QRCode("Hello World!", version=1, eclevel=Low(), mode=UTF8(), mask=0, width=2)

Decode message
using QRDecoders, QRCoders, Test # decode message from QR code matrix code = QRCode("Hello World!", width=0) mat = qrcode(code) info = qrdecode(mat) @test info.message == "Hello World!" @test info == code # decode message from pictures exportqrcode("Hello World!", "test.png") info = qrdecode("test.png") @test info.message == "Hello World!"
Special QR codes

Unicode plot
using QRCoders unicodeplot("Hello World!") # via UnicodePlots.jl # plot using Unicode characters `['β', 'β', 'β', ' ']` unicodeplotbychar("Hello World!") > println
This idea is suggested by notinaboat in the issue#25

pixel drawing: Plot image in a QR code
using TestImages, ImageTransformations, FileIO, ColorTypes # read image img = testimage("cameraman") code = QRCode("HELLO WORLD", version=20) inlen = qrwidth(code)  2 * code.border  15 bitimg = .!(Bool.(round.(Gray.(imresize(img, (inlen, inlen)))))) # draw image inside the QR code mat = imageinqrcode(code, bitimg, rate=0.9) # file export mat > exportbitmat("cameraman.png")
Note that this is not a simple padded image, but is plotted using error correction and free bits. So it is scannable by a normal QR code reader. The idea of plot using free bits and error correction is inspired by ibukisaar.
Other styles are on the way, welcome to contribute!
Final words
Styles of a QR code has a creative room that beyond oneβs imaginations.
However, due to my limited time and energy, I am currently focusing on the implementation of pixel drawing only. Feel free to give your valuable suggestions to help improve this package!
Top comments (4)
Really nice effort to explain and demonstrate QR codes. π
I have two questions.
1) Most smartphone camera apps now have builtin QR code readers. Would the camera app be able to detect these QR codes?
2) If I make a QR code with say "Hello World!" and distribute it to users, do they need a custom Android app to display the "Hello World"?
Thanks.
Nice questions π
There are many standards for QR codes, such as ISO/IEC 18004:2000, 2015 and etc. QRCoders.jl uses the basic part of these standards. So, images generated by QRCoders.jl can be decoded by a common QR code decoder or by QRDecoders.jl.
However, I am planing to add more complex styles to QRCoders, which will bring more noise to the image. In this regard, it requires more of the image detection ability of a decoder.
Some online decoders that might be useful:
Thanks for the responses. All the best for experimenting with Julia. We need more such efforts!
Wow! The final example is really cool, I know how Iβm going to be making my QR codes now. Great work!
We should deploy this as a service using Genie.jl