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On Weight Distributions for a Class of Codes with Parameters of Reed-Muller Codes

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Abstract

We present a new construction method for a doubly exponential class of binary codes with the parameters of Reed–Muller codes. We investigate the weight spectrum and the distance-invariance property of the proposed codes. In the constructed class of codes with the parameters of Reed–Muller codes, we show the existence of codes with the same weight distribution as for a Reed–Muller code and of codes with weight distributions other than this. We establish that all codes with the parameters of the Reed–Muller code which are obtained by the Vasil’ev–Pulatov construction but are distinct from extended perfect codes either are equivalent to the original Reed–Muller codes or have distance distributions different from those.

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Acknowledgments

The authors are grateful to S.V. Agustinovich and V.N. Potapov for drawing the authors' attention to the problem of describing the weight distribution of codes with the parameters of Reed–Muller codes.

Funding

The research was carried out at the expense of the Russian Science Foundation, project no. 22-21-00135, https://rscf.ru/en/project/22-21-00135/

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

    I. Yu. Mogilnykh

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  1. I. Yu. Mogilnykh
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  2. F. I. Solov’eva
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Translated from Problemy Peredachi Informatsii, 2022, Vol. 58, No. 3, pp. 33–44. https://doi.org/10.31857/S0555292322030032

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Mogilnykh, I., Solov’eva, F. On Weight Distributions for a Class of Codes with Parameters of Reed-Muller Codes. Probl Inf Transm 58, 231–241 (2022). https://doi.org/10.1134/S0032946022030036

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  • DOI: https://doi.org/10.1134/S0032946022030036

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