Coding theory

the simplest numeral system, a non-positional numeral system

study of the properties of codes and their fitness for a specific application according to its environment constraints

number of bits that differ between two strings

error-correcting code

error-correcting codes

pattern used within a communications system to represent digital data

class of error correction code

linear error correcting code

error-correcting codes

Data compression theory

limit on data transfer rate

number of nonzero symbols in a string

necessary and sufficient condition for the existence of a prefix code for a given set of codeword lengths

uniquely decodable code where, given a complete and accurate sequence, a receiver can identify each word without requiring a special marker between words

family of error-correcting codes

Entropy encoding

upper bound in coding theory

block code where the circular shifts of each codeword gives another word that belongs to the code

common communications channel model used in coding theory and information theory

algorithm

theorem

thumb|300px|Graphical depiction of the 4 data bits d1 to d4 and 3 parity bits p1 to p3 and which parity bits apply to which data bits In coding theory, Hamming(7,4) is a linear error-correcting code that encodes four bits of data into seven bits by adding three parity bits. It is a member of a larger family of Hamming codes, but the term Hamming code often refers to this specific code that Richard W. Hamming introduced in 1950. At the time, Hamming worked at Bell Telephone Laboratories and was frustrated with the error-prone punched card reader, which is why he started working on error-correct

in coding theory, a limit on the parameters of a code

type of error correcting code

mathematical number sequence

a forward error correction (FEC) code

computer Networking Program

error-correcting codes used in wireless communication

error-correcting code

matrix generating a linear code

algorithm to decode messages

string metric

limit on the parameters of a block code

information theory technique for assigning shorter encoding sequences to more frequently-occurring represented elements

error-correcting codes

part of coding theory

positional numeral system with signed digits; the representation may not be unique

Error correcting algorithm

particular type of Huffman code with unique properties which allow it to be described in a very compact manner

kind of mathematical linear code

limit on the number of codewords in binary codes of given length and minimum distance