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Application of circulant matrices to the construction and decoding of linear codes

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2 Author(s)
Roth, R.M. ; IBM Almaden Res. Center, San Jose, CA, USA ; Lempel, A.

The Fourier transform technique is used to analyze and construct several families of double-circulant codes. The minimum distance of the resulting codes is lower-bounded by 2√r and can be decoded easily employing the standard BCH decoding algorithm or the majority-logic decoder of Reed-Muller codes. A decoding procedure for Reed-Solomon codes is presented, based on a representation of the parity-check matrix by circulant blocks. The decoding procedure inherits both the (relatively low) time complexity of the Berlekamp-Massey algorithm and the hardware simplicity characteristic of Blahut's algorithm. The procedure makes use of the encoding circuit together with a reduced version of Blahut's decoder

Published in:

Information Theory, IEEE Transactions on  (Volume:36 ,  Issue: 5 )

Date of Publication:

Sep 1990

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