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Maximum Intersection of Linear Codes and Codes Equivalent to Linear

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Abstract

We consider linear codes in a space over a finite field with the Hamming metric. A code is called pseudolinear if it is the image of a linear code under an isometric transformation of the space. We derive an upper bound (q - 2)M/q attainable for q ⩾ 3 for the size of the intersection of two different pseudolinear codes of the same size M.

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Acknowledgment

The authors express their gratitude to D. S. Krotov and V. N. Potapov for the fruitful discussions on the topic of the present article.

Funding

The authors were supported by the Russian Foundation for Basic Research (project no. 19-01-00682) and the Program No. I.5.1 of Fundamental Scientific Research of the Siberian Branch of the Russian Academy of Sciences (project no. 0314-2019-0016).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    S. V. Avgustinovich & E. V. Gorkunov

  2. Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090, Russia

    S. V. Avgustinovich & E. V. Gorkunov

Authors
  1. S. V. Avgustinovich
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  2. E. V. Gorkunov
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Corresponding authors

Correspondence to S. V. Avgustinovich or E. V. Gorkunov.

Additional information

Russian Text © The Author(s), 2019, published in Diskretnyi Analiz i Issledovanie Operatsii, 2019, Vol. 26, No. 4, pp. 5-15.

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Avgustinovich, S.V., Gorkunov, E.V. Maximum Intersection of Linear Codes and Codes Equivalent to Linear. J. Appl. Ind. Math. 13, 600–605 (2019). https://doi.org/10.1134/S1990478919040021

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  • DOI: https://doi.org/10.1134/S1990478919040021

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