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The Correspondence Between Projective Codes and 2-weight Codes

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Abstract

We show how to get a 1-1 correspondence between projective linear codes and 2-weight linear codes. A generalization of the construction gives rise to several new ternary linear codes of dimension six.

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References

  1. M. van Eupen, A geometrical construction of the [69, 5, 45] code, preprint.

  2. M. van Eupen and R. Hill, An optimal ternary [69, 5, 45] code and related codes, Designs, Codes & Cryptography, Vol. 4,No. 3 (1994) pp. 271–282.

    Google Scholar 

  3. P. P. Greenough and R. Hill, Optimal linear codes over GF(4), Discrete Mathematics, Vol. 12 (1994) pp. 187–199.

    Google Scholar 

  4. N. Hamada, A survey of recent work on characterization of minihypers in P G(t, q) and nonbinary linear codes meeting the Griesmer bound, J. Combin. Inform. System. Sci., Vol. 18 (1993) pp. 161–191.

    Google Scholar 

  5. R. Hill and D. E. Newton, Some optimal ternary linear codes, Ars Combinatoria, Vol. 25-A (1988) pp. 61–72.

    Google Scholar 

  6. R. Hill and D. E. Newton, Optimal ternary codes, Designs, Codes & Cryptography, Vol. 2 (1992) pp. 137–157.

    Google Scholar 

  7. P. Lizak, Minimum distance bounds for linear codes over GF(3) and GF(4), MSc thesis, University of Salford (1992).

  8. C. L. Mallows, V. Pless and N. J. A. Sloane, Self-dual codes over GF(3), SIAM J. Appl. Math., Vol. 31 (1976) pp. 649–666.

    Google Scholar 

  9. V. Pless, Power moment identities on weight distributions in error correcting codes, Information and Control, Vol. 6 (1963) pp. 147–152.

    Google Scholar 

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Brouwer, A.E., Eupen, M.v. The Correspondence Between Projective Codes and 2-weight Codes. Designs, Codes and Cryptography 11, 261–266 (1997). https://doi.org/10.1023/A:1008294128110

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  • DOI: https://doi.org/10.1023/A:1008294128110

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