Title :
A code decomposition approach for decoding cyclic and algebraic-geometric codes
Author :
Shen, Ba-Zhong ; Tzeng, Kenneth K.
Author_Institution :
Dept. of Comput. Sci. & Electr. Eng., Lehigh Univ., Bethlehem, PA, USA
fDate :
11/1/1995 12:00:00 AM
Abstract :
An approach based on code decomposition and partial transform for constructing algorithms for decoding cyclic codes and algebraic-geometric (AG) codes is introduced. A general decoding procedure applicable to arbitrary linear codes and their subfield subcodes is then developed. In particular, we have developed algorithms for error-and-erasure decoding of cyclic codes up to their actual minimum distance, error-and-erasure decoding of AG codes up to their designed minimum distance, and decoding of subfield subcodes of AG codes (geometric BCH codes). Moreover, a generalization of geometric BCH codes is introduced. It is shown by an example that for a simple class of AG codes, the so-called one-point codes, this generalization brings a better estimate of their minimum distance. It is also shown that the algorithms developed in this paper can be applied to decode these codes up to their estimated minimum distance
Keywords :
BCH codes; algebraic geometric codes; cyclic codes; decoding; linear codes; algebraic-geometric codes; arbitrary linear codes; code decomposition approach; cyclic codes; decoding; error-and-erasure decoding; geometric BCH codes; minimum distance; one-point codes; partial transform; subfield subcodes; Algorithm design and analysis; Australia; Decoding; Error correction; Information theory; Lattices; Linear code;
Journal_Title :
Information Theory, IEEE Transactions on