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Probl. Peredachi Inf., 2007, Volume 43, Issue 1, Pages 32–38 (Mi ppi4)  

This article is cited in 9 scientific papers (total in 9 papers)

Coding Theory

On $\mathbb Z_4$-Linear Codes with Parameters of Reed–Muller Codes

F. I. Solov'eva

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: For any pair of integers $r$ and $m$, $0\le r\le m$, we construct a class of quaternary linear codes whose binary images under the Gray map are codes with the parameters of the classical $r$th-order Reed–Muller code $RM(R,m)$.

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English version:
Problems of Information Transmission, 2007, 43:1, 26–32

Bibliographic databases:

UDC: 621.391.15
Received: 28.03.2006
Revised: 12.10.2006

Citation: F. I. Solov'eva, “On $\mathbb Z_4$-Linear Codes with Parameters of Reed–Muller Codes”, Probl. Peredachi Inf., 43:1 (2007), 32–38; Problems Inform. Transmission, 43:1 (2007), 26–32

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Pujol J., Rifa J., Solov'eva F.I., “Quaternary plotkin constructions and quaternary Reed-Muller codes”, algebra, algebraic algorithms and error-correcting codes, Lecture Notes in Comput. Sci., 4851, Springer, Berlin, 2007, 148–157  crossref  mathscinet  zmath  isi
    2. Pernas J., Pujol J., Villanueva M., “Kernel dimension for some families of quaternary Reed-Muller codes”, Mathematical methods in computer science, Lecture Notes in Comput. Sci., 5393, Springer, Berlin, 2008, 128–141  crossref  mathscinet  zmath  isi
    3. Pujol J., Rifa J., Solov'eva F.I., “On new quaternary Reed-Muller codes”, 2008 IEEE Region 8 International Conference on Computational Technologies in Electrical and Electronics Engineering: SIBIRCON 2008, Proceedings, 2008, 16–19  crossref  isi
    4. F. I. Solov'eva, “On transitive partitions of an $n$-cube into codes”, Problems Inform. Transmission, 45:1 (2009), 23–31  mathnet  crossref  mathscinet  zmath  isi
    5. Pujol J., Rifa J., Solov'eva F.I., “Construction of $\mathbb Z_4$-linear Reed-Muller codes”, IEEE Trans. Inform. Theory, 55:1 (2009), 99–104  crossref  mathscinet  isi  elib
    6. Pernas J., Pujol J., Villanueva M., “Rank for some families of quaternary Reed-Muller codes”, Applied algebra, algebraic algorithms, and error-correcting codes, Lecture Notes in Comput. Sci., 5527, Springer, Berlin, 2009, 43–52  crossref  mathscinet  zmath  isi
    7. Pernas J., Pujol J., Villanueva M., “Classification of some families of quaternary Reed-Muller codes”, IEEE Trans. Inform. Theory, 57:9 (2011), 6043–6051  crossref  mathscinet  isi  elib
    8. Krotov D.S. Villanueva M., “Classification of the Z(2)Z(4)-Linear Hadamard Codes and Their Automorphism Groups”, IEEE Trans. Inf. Theory, 61:2 (2015), 887–894  crossref  mathscinet  isi  elib
    9. Gillespie N.I. Praeger Ch.E., “New Characterisations of the Nordstrom-Robinson Codes”, Bull. London Math. Soc., 49:2 (2017), 320–330  crossref  mathscinet  zmath  isi  scopus
  • Проблемы передачи информации Problems of Information Transmission
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