BCH code

In <a href="/facts/Coding_theory/SBqStoGL">coding theory</a>, the Bose–Chaudhuri–Hocquenghem codes (BCH codes) form a class of <a href="/facts/Cyclic_code/LmhezpnR">cyclic</a> <a href="/facts/Error_correction_code/cLUTUJrA">error-correcting codes</a> that are constructed using <a href="/facts/Polynomial/Lzak8VVx">polynomials</a> over a <a href="/facts/Finite_field/UkMGJo3m">finite field</a> (also called a <a href="/facts/Finite_field/UkMGJo3m">Galois field</a>). BCH codes were invented in 1959 by French mathematician <a href="/facts/Alexis_Hocquenghem/E3Rh7GMV">Alexis Hocquenghem</a>, and independently in 1960 by <a href="/facts/Raj_Chandra_Bose/RI0WHXIV">Raj Chandra Bose</a> and <a href="/facts/D._K._Ray-Chaudhuri/bPCkPTWu">D. K. Ray-Chaudhuri</a>. The name Bose–Chaudhuri–Hocquenghem (and the acronym BCH) arises from the initials of the inventors' surnames (mistakenly, in the case of Ray-Chaudhuri).
One of the key features of BCH codes is that during code design, there is a precise control over the number of symbol errors correctable by the code. In particular, it is possible to design binary BCH codes that can correct multiple bit errors. Another advantage of BCH codes is the ease with which they can be decoded, namely, via an <a href="/facts/Abstract_algebra/YNNE1CNz">algebraic</a> method known as <a href="/facts/Syndrome_decoding/A0x9Dpgq">syndrome decoding</a>. This simplifies the design of the decoder for these codes, using small low-power electronic hardware.
BCH codes are used in applications such as satellite communications, <a href="/facts/Compact_disc/g51GRloc">compact disc</a> players, <a href="/facts/DVD/7fJsHJrN">DVDs</a>, <a href="/facts/Disk_storage/hnsXRb5X">disk drives</a>, <a href="/facts/USB_flash_drive/Jv0qmTCF">USB flash drives</a>, <a href="/facts/Solid-state_drive/aMHBy8gU">solid-state drives</a>, and <a href="/facts/Bar_codes/Mkh4cCTp">two-dimensional bar codes</a>.

BCH code open-in-new

BCH code