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
M. van Eupen, A geometrical construction of the [69, 5, 45] code, preprint.
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.
P. P. Greenough and R. Hill, Optimal linear codes over GF(4), Discrete Mathematics, Vol. 12 (1994) pp. 187–199.
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.
R. Hill and D. E. Newton, Some optimal ternary linear codes, Ars Combinatoria, Vol. 25-A (1988) pp. 61–72.
R. Hill and D. E. Newton, Optimal ternary codes, Designs, Codes & Cryptography, Vol. 2 (1992) pp. 137–157.
P. Lizak, Minimum distance bounds for linear codes over GF(3) and GF(4), MSc thesis, University of Salford (1992).
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.
V. Pless, Power moment identities on weight distributions in error correcting codes, Information and Control, Vol. 6 (1963) pp. 147–152.
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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