General principles for the algebraic decoding of cyclic codes

  • Authors:

  • Xuemin Chen;I. S. Reed;T. Helleseth;T. K. Truong

  • Affiliations:

  • Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA, USA;-;-;-

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 1994

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Abstract

This paper provides two theorems for decoding all types of cyclic codes. It is shown that from a polynomial ideal point of view, the decoding problems of cyclic codes are closely related to the monic generators of certain polynomial ideals. This conclusion is also generalized to the decoding problems of algebraic geometry codes.