Abstract
Balanced generalized weight matrices are used to construct optimal constant weight codes that are monomially inequivalent to codes derived from the classical simplex codes. What’s more, these codes can be assumed to be generated entirely by \(\omega \)-shifts of a single codeword where \(\omega \) is a primitive element of a Galois field. Additional constant weight codes are derived by projecting onto subgroups of the alphabet sets. These too are shown to be optimal.
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Acknowledgements
The authors wish to acknowledge anonymous referees for their constructive comments. Hadi Kharaghani is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).
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HK, TP, and VT worked together, TP drafted the first version, HK the second version and VT the third version.
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Communicated by M. Buratti.
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Kharaghani, H., Pender, T. & Tonchev, V. On optimal constant weight codes derived from \(\omega \)-circulant balanced generalized weighing matrices. Des. Codes Cryptogr. (2024). https://doi.org/10.1007/s10623-024-01414-w
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DOI: https://doi.org/10.1007/s10623-024-01414-w
Keywords
- Constant weight code
- Equidistant nonlinear code
- Inequivalent codes
- Optimal code
- \(\omega \)-circulant balanced generalized weighing matrix