Two dimensional code coding theory

Coding theory can be regarded as Galois domain （Galois Field）[18,30-31] One of the IT application , Its production is entirely based on industrial demand , The sign is 1948 year Shannon Published papers “The Mathematical Theory of communication” and 1950 The invention of Hamming code , So far, it has been close to 70 Years of history .
But from 1950 A long time after the invention of Hamming code in , The development of coding theory has stagnated . It's over again.
10 year , With the progress of Industrial Technology , The demand for communication technology is also increasing , In modulation 、 Source coding and other fields
The theory of intersection coding is active again . at present , Coding theory is still in its heyday .
A good code system , Simply put, the coding efficiency is high 、 Large minimum distance 、 The algorithm of coding and decoding is simple
The system of . At present, it has been widely used ： Linear block code 、 Convolutional code 、Turbo code 、 Space-time code is a good generation
Code system .
According to Occam's razor law , The most widely used is often the simplest . At present, the popular good code should
The most widely used is the simplest linear block code , Linear block codes can be divided into many kinds , The simplest of them ,
It is also the most widely used code called cyclic code . The cyclic code is composed of Eugene Prange stay 1957 Invented in .
The proposal immediately received the attention of the industry , And then produced a large number of related achievements .
One of the most representative achievements , It's in 1960 Was proposed in , Mature in the same year . The core idea is ： A conjugate root system is generated by primitive polynomials , The root system is just a cyclic code , And it can correct more than one mistake , This is it. BCH code . According to the number of elements of the finite field based on ,BCH Codes can be roughly divided into binary BCH Code and multiple BCH code , Pluralistic origin BCH code （ Primitive is code root ） be called Reed-Solomon code [30,32], Its symbol field and error location field are the same , Therefore, the root polynomial is also the minimum polynomial , This feature can construct cyclic codes with large minimum distance , It brings a lot of convenience to encoding and decoding .

reference ：
[1] Feng Wei . Research on fast recognition technology of two-dimensional code for visual location [D]. Shandong University of technology ,2018.