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. 
Efficient generation technique for polynomial codesets
TLDR
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. Expand
A tutorial on CRC computations
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 areExpand
Arithmetic Error Detecting Codes for Communications Links Involving Computers
TLDR
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. Expand
Experimental Studies of Polynomial Codes in Concurrent Error Detection Systems of Combinational Logical Circuits
TLDR
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. Expand
Parallel CRC generation
TLDR
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. Expand
Universal Crypting-Decrypting Algorithm
TLDR
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. Expand
A practical class of polynomial codes
TLDR
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. Expand
A Note on Extending Certain Codes to Correct Error Bursts in Longer Messages
TLDR
This note presents a simple method of constructing burst correcting codes, and supplies a geometric interpretation of the method. Expand
Isomorphism between Linear Codes and Arithmetic Codes for Safe Data Processing in Embedded Software Systems
TLDR
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. Expand
Error-burst detection with tandem CRCs
TLDR
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. Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 11 REFERENCES
A note off two binary signaling alphabets
  • D. Slepian
  • Computer Science
  • IRE Trans. Inf. Theory
  • 1956
TLDR
A generalization of Hamming's single error correcting codes is given along with a simple maximum likelihood detection scheme for Reed-Muller alphabets and a new detection scheme is presented for them. Expand
Codes for the correction of 'clustered' errors
  • S. Reiger
  • Computer Science
  • IRE Trans. Inf. Theory
  • 1960
A method is described which permits the systematic construction of codes capable of error-free transmission, provided errors occur in "clusters" of limited duration. The method is valid for errorExpand
Encoding and error-correction procedures for the Bose-Chaudhuri codes
TLDR
A simple error-correction procedure for binary codes which for arbitrary m and t are t -error correcting and have length 2^m - 1 of which no more than mt digits are redundancy is described. Expand
Error Correcting Codes for Correcting Bursts of Errors
It is observed that the codes of Abramson, Melas and others are essentially described by the characteristic equation that a certain matrix satisfies. Consequently it is found that transformations ofExpand
An Error-Correcting Encoder and Decoder of High Efficiency
TLDR
A group effort has demonstrated the applicability of regenerative shift register sequences to error-correcting codes and shown that the interrelationships between the bits of these binary sequences can be used to design a decoder of extreme simplicity. Expand
On A Class of Error Correcting Binary Group Codes
TLDR
A general method of constructing error correcting binary group codes is obtained and an example is worked out to illustrate the method of construction. Expand
A New Group of Codes for Correction of Dependent Errors in Data Transmission
  • C. Melas
  • Computer Science
  • IBM J. Res. Dev.
  • 1960
TLDR
Because each parity-bit group is derived by using maximum-length shift-register sequences, rather than by storing a decoding table, the implementation of these codes is relatively simple, as shown in an example of a three-bit-wide burst-correcting code. Expand
A class of binary signaling alphabets
A class of binary signaling alphabets called “group alphabets” is described. The alphabets are generalizations of Hamming's error correcting codes and possess the following special features: (1) allExpand
Further Results on Error Correcting Binary Group Codes
TLDR
The present paper generalizes the methods of the earlier paper and gives a method of constructing a t-error correcting code with n places for any arbitrary n and k = n − R(m,t) ≧ [(2m − 1)/c] − mt information places where m is the least integer such that cn = 2m −1 for some integer c. Expand
...
1
2
...