An Introduction to Anticodes

  • P. G. Farrell
Part of the International Centre for Mechanical Sciences book series (CISM)


The N code-words of a binary block error-correcting code1,2 of block length n can be tabulated as the rows of an Nxn matrix: this is the code-book of the code. The N rows of the code-book are the codewords; the n columns of the code-took are also of interest, and may be called the code-columns.


Generator Matrix Linear Code Block Length Parity Check Code Word 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Peterson, W.W. and Weldon, E.J., Error-correcting codes, M.I.T., 1972.Google Scholar
  2. 2.
    MacWilliams, F.J. and Sloane, N.J.A, The Theory of Error-Correcting Codes, Vols. I & II, North-Holland, 1977.zbMATHGoogle Scholar
  3. 3.
    Hamming, R.W., Error-correcting and error-detecting codes, Bell Syst. Tech. Jour., 1950, Vol. 26, pp. 147–160.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Longo, G., An introduction to algebraic coding theory, CISM Report No. 23, April 1977.Google Scholar
  5. 5.
    Farrell, P.G., Coding for noisy data links, Ph.D. Thesis, University of Cambridge, 1969.Google Scholar
  6. 6.
    Golamb, S.W. (Ed), Digital Communications with Space Applications, Prentice-Hall, 1964.Google Scholar
  7. 7.
    Plotkin, M., Binary codes with specified minimum distance, IRE Trans., 1960, Vol. IT-6, pp. 445–450.MathSciNetGoogle Scholar
  8. 8.
    Griesmer, J.H., A bound for error-correcting codes, I.B.M. Jour., 1960, Vol. 4, No. 5, p. 532.MathSciNetzbMATHGoogle Scholar
  9. 9.
    Solaren, G. and Stiffler, V.J., Algebraically punctured cyclic code, Information and Control, 1965, Vol. 8, pp. 170–179.MathSciNetCrossRefGoogle Scholar
  10. 10.
    Berlekamp, E.R., Algebraic coding theory, McGraw-Hill, 1968.zbMATHGoogle Scholar
  11. 11.
    Hashim, A.A., Maximum distance bounds for linear anticodes, Proc. IEE, Vol. 123, No. 3, pp. 189–190, March, 1976.MathSciNetGoogle Scholar
  12. 12.
    Gilbert, E.N., A comparison of signalling alphabets, BSTJ, Vol. 31, No. 3, May, 1952, pp. 504–522.Google Scholar
  13. 13.
    Farrell, P.G., Linear binary antioodes, Elec. Letters, 1970, Vol. 6, No. 13, pp. 419–421.CrossRefzbMATHGoogle Scholar
  14. 14.
    Farrell, P.G. and Farrag, A., Further properties of linear binary anticodes, Elec. Letters, Vol. 10, No. 16, 8 Aug. 1974, p. 340.CrossRefGoogle Scholar
  15. 15.
    Farrell, P.G. and Farrag, A., New error-control codes derived frcm antioodes, presented at IEEE Symp. on Info. Theory, Ronneby, June 1976.Google Scholar
  16. 16.
    Farrag, A., Anticodes and optimum error-correcting codes, Ph.D. Thesis, University of Kent at Canterbury, 1976.Google Scholar
  17. 17.
    Maki, G.K. and Traoey, J.H., Maximum distance linear codes, IEEE Trans., 1971, Vol. IT-17, No. 5, p. 637.Google Scholar
  18. 18.
    Reddy, S.M., On block codes with specified maximum distance, IEEE Trans., 1912, Vol. IT-18, No. 6, pp. 823–824.Google Scholar
  19. 19.
    Hashim, A.A. and Podzniakov, V.S., On the stacking techniques of linear codes, paper submitted for publication to 3EE.Google Scholar
  20. 20.
    Baumert, L.D. and McEliece, R.J., A note on the Griesmer bound, IEEE Trans., Vol. TP-19, pp. 134–135, No. 1, January 1973.MathSciNetzbMATHGoogle Scholar
  21. 21.
    Helgert, H.J. and Stinaff, R.D., Minimum-distance bounds for binary linear codes, IEEE Trans., 1973, Col. IT-19, No. 3, pp. 344–356.MathSciNetzbMATHGoogle Scholar
  22. 22.
    Reed, I.S., A class of multiple-error-correcrting codes and the decoding scheme, IRE Trans., Vol. IT-4, No. 5, Sept. 1954, p. 38.Google Scholar
  23. 23.
    Belov, B.I., Logachev, V.N. and Sandimirov, V.P., The constructicn of a class of binary linear codes which achieve the Varshamov-Griesmer bound, Prob. Pered. Infor., Vol. 10, No. 3, pp. 36–44.Google Scholar
  24. 24.
    Patel, A.M., Maximal group codes with specified miniinum distance, I.B.M. Jour. Res. Dev., Vol. 14, No. 4, pp. 434–443.Google Scholar
  25. 25.
    MacWilliams, J., Error-correcting oodes for multiple-level transmission, Bell. Syst. Tech. Jour., 1961, Vol. 40, pp. 281–308.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 1979

Authors and Affiliations

  • P. G. Farrell
    • 1
  1. 1.Electronics LaboratoriesThe university of Kent at CanterburyCanterbury, KentEngland

Personalised recommendations