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Diskretn. Anal. Issled. Oper., Ser. 1, 2000, Volume 7, Number 4, Pages 78–90 (Mi da281)  

This article is cited in 23 scientific papers (total in 23 papers)

$Z_4$-linear perfect codes

D. S. Krotov

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

Full text: PDF file (1308 kB)

Bibliographic databases:
UDC: 519.725
Received: 03.07.2000

Citation: D. S. Krotov, “$Z_4$-linear perfect codes”, Diskretn. Anal. Issled. Oper., Ser. 1, 7:4 (2000), 78–90

Citation in format AMSBIB
\Bibitem{Kro00}
\by D.~S.~Krotov
\paper $Z_4$-linear perfect codes
\jour Diskretn. Anal. Issled. Oper., Ser.~1
\yr 2000
\vol 7
\issue 4
\pages 78--90
\mathnet{http://mi.mathnet.ru/da281}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1815984}
\zmath{https://zbmath.org/?q=an:1008.94025}


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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. V. A. Zinov'ev, D. V. Zinov'ev, “Binary Extended Perfect Codes of Length 16 by the Generalized Concatenated Construction”, Problems Inform. Transmission, 38:4 (2002), 296–322  mathnet  crossref  mathscinet  zmath
    2. N. N. Tokareva, “Representation of $\mathbb Z_4$-Linear Preparata Codes by Means of Vector Fields”, Problems Inform. Transmission, 41:2 (2005), 113–124  mathnet  crossref  mathscinet  zmath
    3. F. I. Solov'eva, “On Construction of Transitive Codes”, Problems Inform. Transmission, 41:3 (2005), 204–211  mathnet  crossref  mathscinet  zmath
    4. F. I. Solov'eva, “On $\mathbb Z_4$-Linear Codes with Parameters of Reed–Muller Codes”, Problems Inform. Transmission, 43:1 (2007), 26–32  mathnet  crossref  mathscinet  isi  elib  elib
    5. J. Appl. Industr. Math., 2:4 (2008), 566–584  mathnet  crossref  zmath
    6. Krotov D.S., “On Z(2)k-dual binary codes”, IEEE Trans Inform Theory, 53:4 (2007), 1532–1537  crossref  mathscinet  zmath  isi  elib  scopus
    7. N. N. Tokareva, “Description of $k$-bent functions in four variables”, J. Appl. Industr. Math., 3:2 (2009), 284–289  mathnet  crossref  mathscinet  zmath
    8. N. N. Tokareva, “On Quadratic Approximations in Block Ciphers”, Problems Inform. Transmission, 44:3 (2008), 266–286  mathnet  crossref  mathscinet  zmath  isi
    9. Solov'eva F.I., “On perfect binary codes”, Discrete Appl Math, 156:9 (2008), 1488–1498  crossref  mathscinet  zmath  isi  scopus
    10. Rifa J., Solov'eva F.I., Villanueva M., “On the intersection of Z(2)Z(4)-additive perfect codes”, IEEE Trans Inform Theory, 54:3 (2008), 1346–1356  crossref  mathscinet  zmath  isi  elib  scopus
    11. Ahlswede R., Solov'eva F.I., “A Diametric Theorem in Z(m)(n) for Lee and Related Distances”, Coding Theory and Applications, Proceedings, Lecture Notes in Computer Science, 5228, 2008, 1–10  crossref  zmath  isi  scopus
    12. 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  scopus
    13. Tokareva N.N., “K-Bent Functions: From Coding Theory to Cryptology”, 2008 IEEE Region 8 International Conference on Computational Technologies in Electrical and Electronics Engineering: SIBIRCON 2008, Proceedings, IEEE, 2008, 36–40  crossref  isi  scopus
    14. 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
    15. Pujol J., Rifa J., Solov'eva F.I., “Construction of Z(4)-Linear Reed-Muller Codes”, IEEE Trans Inform Theory, 55:1 (2009), 99–104  crossref  mathscinet  zmath  isi  elib  scopus
    16. Borges J., Mogilnykh I.Yu., Rifa J., Solov'eva F.I., “Structural Properties of Binary Propelinear Codes”, Adv. Math. Commun., 6:3 (2012), 329–346  crossref  mathscinet  zmath  isi  elib  scopus
    17. G. K. Guskov, F. I. Solov'eva, “On extremely transitive extended perfect codes”, J. Appl. Industr. Math., 8:1 (2014), 53–62  mathnet  crossref  mathscinet
    18. Krotov D.S., Potapov V.N., “Propelinear 1-Perfect Codes From Quadratic Functions”, IEEE Trans. Inf. Theory, 60:4 (2014), 2065–2068  crossref  mathscinet  zmath  isi  elib  scopus
    19. 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  zmath  isi  elib  scopus
    20. Borges J., Fernandez-Cordoba C., “There Is Exactly One Z(2)Z(4)-Cyclic 1-Perfect Code”, Des. Codes Cryptogr., 85:3 (2017), 557–566  crossref  mathscinet  zmath  isi  scopus
    21. 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
    22. Krotov D.S., “On the Automorphism Groups of the -Linear 1-Perfect and Preparata-Like Codes”, Des. Codes Cryptogr., 83:1 (2017), 169–177  crossref  mathscinet  zmath  isi  scopus
    23. Ozkan M., Oke F., “On Codes Written By Matrices Lexicographically Ordered”, 6Th International Eurasian Conference on Mathematical Sciences and Applications (Iecmsa-2017), AIP Conference Proceedings, 1926, eds. Tosun M., Ersoy S., Ilarslan K., Amer Inst Physics, 2018, UNSP 020035  crossref  isi  scopus
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