Title :
A generalized DFT for Abelian codes over Zm
Author :
Rajan, B. Sundar ; Siddiqi, M.U.
Author_Institution :
Dept. of Electr. Eng., Indian Inst. of Technol., New Delhi, India
fDate :
11/1/1994 12:00:00 AM
Abstract :
A generalized discrete Fourier transform defined over an appropriate extension ring is given that is suitable to characterize Abelian codes over residue class integer rings Zm. The characterization is in terms of generalized discrete Fourier transform components taking values from certain ideals of the extension ring. It is shown that the results known for cyclic codes over Zm, like the simple characterization of dual and self-dual codes and the nonexistence of self-dual codes for certain values of code parameters, extend to Abelian codes over Zm as well
Keywords :
cyclic codes; discrete Fourier transforms; dual codes; Abelian codes; code parameters; cyclic codes; discrete Fourier transform; dual codes; extension ring; generalized DFT; residue class integer rings; self-dual codes; Binary codes; Error correction codes; Iterative decoding; Lattices; Maximum likelihood decoding; Partitioning algorithms; Performance loss;
Journal_Title :
Information Theory, IEEE Transactions on
