Dual Code - Self-dual Codes

Self-dual Codes

A self-dual code is one which is its own dual. This implies that n is even and dim C = n/2. If a self-dual code is such that each codeword's weight is a multiple of some constant, then it is of one of the following four types:

  • Type I codes are binary self-dual codes which are not doubly even. Type I codes are always even (every codeword has even Hamming weight).
  • Type II codes are binary self-dual codes which are doubly even.
  • Type III codes are ternary self-dual codes. Every codeword in a Type III code has Hamming weight divisible by 3.
  • Type IV codes are self-dual codes over F4. These are again even.

Codes of types I, II, III, or IV exist only if the length n is a multiple of 2, 8, 4, or 2 respectively.

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