# Transform Techniques for Error Control Codes

@article{Blahut1979TransformTF, title={Transform Techniques for Error Control Codes}, author={Richard E. Blahut}, journal={IBM J. Res. Dev.}, year={1979}, volume={23}, pages={299-315} }

By using the theory of finite field Fourier transforms, the subject of error control codes is described in a language familiar to the field of signal processing. The many important uses of spectral techniques in error control are summarized. Many classes of linear codes are given a spectral interpretation and some new codes are describe. Several alternative encoder/ decoder schemes are described by frequency domain reasoning. In particular, an errors-and-erasures decoder for a BCH code is…

## 201 Citations

### Codes For Error Correction Based Upon Interpolation Of Real-number Sequences

- Computer ScienceNineteeth Asilomar Conference on Circuits, Systems and Computers, 1985.
- 1985

It will be shown that correction of burst errors in coded signals can be accomplished by error-trapping structures, and the complete coding system is conveniently realizable by general-purpose, programmable, digital signal or image processors.

### Coding of Real-Number Sequences for Error Correction: A Digital Signal Processing Problem

- Computer ScienceIEEE J. Sel. Areas Commun.
- 1984

A large class of block and convolutional real-number single-error-correcting codes, derived from similar codes over GF(p) , are presented and it is shown that maximum distance separable real- number BCH codes exist for all nontrivial values of N and K.

### Extended-BCH codes using fourier transform over a finite field

- Computer Science
- 1983

It is shown that when the code is constructed by this method, the fast Fourier transform algorithm can be applied to a wider range of code lengths than before in syndrome-calculation.

### On Blahut's Decoding Algorithms for Two-Dimensional BCH Codes

- Computer ScienceIEEE Trans. Inf. Theory
- 1998

It is shown that Blahut's decoding algorithms have optimal error-correcting capability and improved decoding algorithms are presented, which have less computational complexity.

### A transform approach to Goppa codes

- Computer ScienceIEEE Trans. Inf. Theory
- 1987

It is shown how the class of Goppa codes can be easily decoded in the context of this transformation by using the Berlekamp-Massey decoding algorithm.

### Generalized minimum distance decoding with arbitrary error, erasure tradeoff

- Computer Science
- 2012

A means of expressing their error-correcting capabilities by a unified function, the Generalized Decoding Radius is introduced, which considers the decoding radius of GMD decoding, i.e., the maximum number of errors that are correctable with guarantee.

### The application of Walsh transform for forward error correction

- Computer Science1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258)
- 1999

A novel class of forward error correcting codes constructed using the discrete Walsh transform are presented, defined on the field of real numbers, and compared to those of the well-known BCH and RS codes.

### A Reed-Solomon code simulator and periodicity algorithm

- Computer Science
- 1994

The periodicity algorithm is introduced and its validity is verified by exhaustive computer simulations and it is concluded that the periodicity algorithms is the optimal solution for both decoding time and memory space.

### Fast Transform for Decoding Both Errors and Erasures of Reed-Solomon Codes Over GF for

- Computer Science
- 2006

The complexity of the transform-domain decoder for correcting both errors and era- sures of the Reed-Solomon codes of block length over GF for is reduced substantially from the pre- vious time- domain decoder.

### Fast Transform for Decoding Both Errors and Erasures of Reed – Solomon Codes Over GF ( 2 m ) for 8 m 10

- Computer Science
- 2006

In this letter, it is shown that a fast, prime-factor discrete Fourier transform (DFT) algorithm can be modified to compute Fourier-like transforms of long sequences of 2 1 points over GF(2 ), where…

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