The Telecommunication area has the Hamming code as a family of linear error-correcting systems in place, and they can detect up to two-bit error types and also correct one-bit error types with having to be the detection of them taking place for any uncorrected errors which may exist. By contrast, the most straightforward Parity Code cannot fix any form of errors but can only detect and odd numbers orbits in mistakes. These code types are classed as perfect codes that are because they give out the highest possible rate for any kinds of systems with there lbock length and minimum distance of three.
The reason for this being invented in the 1950s was a way to allow automatic correcting of errors caused by punched card readers.
The full name of the creator of this a guy called Richard Wesley Hamming who was born in Chicago Illinois February 11, 1915, was a brilliant Dutch Mathematician whos work had many moral implications for a computer engineering or the Telecommunications industry.
The Contributions he made include the “Hamming Code” which provides for people making use of the Hamming Matrix or the Hamming Windows or Hamming Numbers or Sphere packing or Hamming Bound and the Hamming Distance as the main factors into how to understand this valuable tool to improve the coding systems of businesses.
The man went to the University of Chicago called the University of Nebraska and the University of Illinois at Urbana Champaign where he wrote his Doctoral thesis in Mathematics under the supervision of Waldemar Trjitzinsky 1901-!973.
The principle of this idea is to allow 7.4, which is linear error-correcting code to take place that will encode four bits of data into seven bits by adding in three parity bits. At the time of this great man coming up with this idea worked at Bell Telephone Laboratories and was annoyed with the error-prone punched card reader, which is why he started working on way to fix this problem. The code adds in three additional check bits to every four bits of data
The Algorithm can correct any single bit of mistakes or single bit or two bit errors. The main goal of the system is to create a set of partial bits that can overlap so that a single bit error can be shown and fixed quickly.
These rows are used to process the Syndrome vectors at the receiving point, and if the Syndrome factor is null vector all zeros, then the received word is error-free. If non-zero, then the value will tell what bit has been flipped.
Like some other correction codes in place, this one makes use of the idea of parity and parity bits which that can be added into data so that validity of the data can be checked when it read or after the information has been processed by transmission.
Computing involves the counting of numbers of ones in a unit of data and adding either a zero or one called a “Parity bit” to make the count odd (For Odd parity) or even (For even parity)
The data can be shown incorrectly if the data bit has been flipped by the noise in the line, for example, purpose says whatis.techtarget.com or the web 5,345.
The most significant factor in working out the Hamming code is the use of extra parity bits to allow the identification of a single error to be shown
An example is shown below which is
1001010 create the data word leaving spaces for the parity bits __1__001_1010 which can calculate each parity bit (a represents the bit position being set):
Finding and fixing the wrong part can do relatively easy, and you can learn from reading this article