Abstract
We define and study a class of Reed–Muller type error-correcting codes obtained from elementary symmetric functions in finitely many variables. We determine the code parameters and higher weight spectra in the simplest cases.
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The authors sincerely thank the anonymous referees for their careful reading the initial version of this article and providing us with some important suggestions towards improving the article. They also thank Hiram Lopez for their comments and suggestions on this article.
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Communicated by P. Charpin.
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M. Datta is partially supported by a seed grant from Indian Institute of Technology Hyderabad and a Start-up Research Grant (File no. SRG/2021/001177/PMS) from Science and Engineering Research Board (India). M. Datta and T. Johnsen have been partially supported by Grant 280731 from the Research Council of Norway, and by the Project “Pure Mathematics in Norway” through the Trond Mohn Foundation and Tromsø Research Foundation.
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Datta, M., Johnsen, T. Codes from symmetric polynomials. Des. Codes Cryptogr. 91, 747–761 (2023). https://doi.org/10.1007/s10623-022-01123-2
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DOI: https://doi.org/10.1007/s10623-022-01123-2