# Cyclic Codes for Error Detection

@article{Peterson1961CyclicCF, title={Cyclic Codes for Error Detection}, author={W. Wesley Peterson and D. T. Brown}, journal={Proceedings of the IRE}, year={1961}, volume={49}, pages={228-235} }

Cyclic codes are defined and described from a new viewpoint involving polynomials. The basic properties of Hamming and Fire codes are derived. The potentialities of these codes for error detection and the equipment required for implementing error detection systems using cyclic codes are described in detail.

## 197 Citations

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- Computer Science
- 1976

The letter introduces a new technique for the generation of a set of polynomial codewords that is simple to apply and can form the basis for set generation by a minicomputer or microprocessor.

### A tutorial on CRC computations

- Computer ScienceIEEE Micro
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The theory of cyclic redundancy codes (CRS) is reviewed. Four software algorithms for performing CRC computations are described: table lookup, reduced table lookup, on-the-fly, and wordwise. They are…

### Arithmetic Error Detecting Codes for Communications Links Involving Computers

- Computer Science
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Arithmetic-burst-error detecting codes are presented here which are easily implemented by standard arithmetic computer instructions and it is conjectured that the fraction of undetected error bursts is of the same order as that for cyclic codes.

### Experimental Studies of Polynomial Codes in Concurrent Error Detection Systems of Combinational Logical Circuits

- Computer Science2018 IEEE East-West Design & Test Symposium (EWDTS)
- 2018

The authors of the article established the key features of error detection by polynomial codes, the account of which is advisable when building the systems with fault detection.

### Parallel CRC generation

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- 1990

A method of designing hardware parallel encoders for CRCs that is based on digital system theory and z-transforms is presented, which allows designers to derive the logic equations of the parallel encoder circuit for any generator polynomial.

### Universal Crypting-Decrypting Algorithm

- Computer Science
- 2011

The universal algorithm for the generation of cyclic code for an n bit binary word is presented, which is important for the built in self test (BIST) and for memory ROM testing.

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- Computer Science
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A new class of polynomial codes is described for which a correspondence between n-bit data characters andPolynomial coefficients is defined, which may be easily implemented with hardware or with processor character manipulations.

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- Computer ScienceIBM J. Res. Dev.
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This note presents a simple method of constructing burst correcting codes, and supplies a geometric interpretation of the method.

### Isomorphism between Linear Codes and Arithmetic Codes for Safe Data Processing in Embedded Software Systems

- Computer ScienceComput. Informatics
- 2014

Combination of the advantages of both coding mechanisms will increase the error detection capability in safety critical applications for embedded systems by detection and correction of arbitrary hardware faults.

### Error-burst detection with tandem CRCs

- Computer ScienceIEEE Trans. Commun.
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The authors investigate the efficacy of using two different cyclic redundancy check (CRC) codes in tandem to increase error-burst detecting capability and find that strengthened CRC codes can readily be obtained using existing devices.

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