Projective two-weight code 


A projective code whose codewords all have one of two possible nonzero Hamming weights.

There is a correspondence between projective two-weight codes, projective two-character sets, and certain strongly regular graphs [1]. As such, projective two-weight codes have been classified and can be constructed out of quadrics [2,3], maximal arcs and hyperovals, Baer spaces, or Hermitian quadrics [4]. There are also several sporadic examples [4; Table 19.1].





Ph. Delsarte, “Weights of linear codes and strongly regular normed spaces”, Discrete Mathematics 3, 47 (1972) DOI
A. Ashikhmin and A. Barg, “Binomial moments of the distance distribution: bounds and applications”, IEEE Transactions on Information Theory 45, 438 (1999) DOI
N. Hamilton, “Strongly regular graphs from differences of quadrics”, Discrete Mathematics 256, 465 (2002) DOI
A. E. Brouwer, "Two-weight Codes." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
N. Tzanakis and J. Wolfskill, “The diophantine equation x2 = 4qa2 + 4q + 1, with an application to coding theory”, Journal of Number Theory 26, 96 (1987) DOI
A. E. Brouwer and H. Van Maldeghem, Strongly Regular Graphs (Cambridge University Press, 2022) DOI
R. A. Games, “The packing problem for projective geometries over GF(3) with dimension greater than five”, Journal of Combinatorial Theory, Series A 35, 126 (1983) DOI
Rudolf Schürer and Wolfgang Ch. Schmid. “Denniston Codes.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2015-09-03.
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Zoo Code ID: projective_two_weight

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“Projective two-weight code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023.
@incollection{eczoo_projective_two_weight, title={Projective two-weight code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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“Projective two-weight code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023.