LINEAR BLOCK CODES

     Codeword Structure :
      Block codes accept a block of k message bits and produce a block of n coded bits. By predetermined rules, n-k redundant bits are added to the k message bits to form the n coded bits. These codes are referred to as (n, k) block codes.

Example: a (7,4) Hamming code.
Table 2.2: Codewords of a (7,4) Hamming Code

     Block codes in which the message bits are included in unaltered form are called systematic codes. Figure 2.1 shows codeword structure for systematic codes.

Generator Matrix G and Encoding operation :
      Parity bits are linear sum of the message bits: bi = p0im0 + p1im1 + … + pk-1,i mk-1 ( +: modulo-2 addition). It can also be written as:

    b = mP .....(2.1)

Generator Matrix is a k´n matrix defined as
, where              ......(2.2)
Encoding operation is defined as

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