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Probl. Peredachi Inf., 2004, Volume 40, Issue 2, Pages 19–36 (Mi ppi130)  

This article is cited in 4 scientific papers (total in 4 papers)

Coding Theory

On Weight Distributions of Cosets of Goethals-Like Codes

V. A. Zinov'eva, T. Hellesethb

a Institute for Information Transmission Problems, Russian Academy of Sciences
b University of Bergen

Abstract: We study weight distributions of shifts of codes from a well-known family: the 3-error-correcting binary nonlinear Goethals-like codes of length $n=2^m$, where $m\geq 6$ is even. These codes have covering radius $\rho=6$. We know the weight distribution of any shift of weight $i=1,2,3,5$, or 6. For a shift of weight 4, the weight distribution is uniquely defined by the number of leaders in this shift, i.e., the number of vectors of weight 4. We also consider the weight distribution of shifts of codes with minimum distance 7 obtained by deleting any one position of a Goethals-like code of length $n$.

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English version:
Problems of Information Transmission, 2004, 40:2, 118–134

Bibliographic databases:

UDC: 621.391.15
Received: 10.12.2002
Revised: 26.02.2004

Citation: V. A. Zinov'ev, T. Helleseth, “On Weight Distributions of Cosets of Goethals-Like Codes”, Probl. Peredachi Inf., 40:2 (2004), 19–36; Problems Inform. Transmission, 40:2 (2004), 118–134

Citation in format AMSBIB
\Bibitem{ZinHel04}
\by V.~A.~Zinov'ev, T.~Helleseth
\paper On Weight Distributions of Cosets of Goethals-Like Codes
\jour Probl. Peredachi Inf.
\yr 2004
\vol 40
\issue 2
\pages 19--36
\mathnet{http://mi.mathnet.ru/ppi130}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2099006}
\zmath{https://zbmath.org/?q=an:1112.94032}
\transl
\jour Problems Inform. Transmission
\yr 2004
\vol 40
\issue 2
\pages 118--134
\crossref{https://doi.org/10.1023/B:PRIT.0000043926.60991.7e}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. J. Appl. Industr. Math., 2:3 (2008), 426–431  mathnet  crossref  mathscinet  zmath
    2. Tokareva N., “An upper bound for the number of uniformly packed codes”, 2007 IEEE International Symposium on Information Theory Proceedings, 2007, 346–349  crossref  isi
    3. Krotov D.S., “On weight distributions of perfect colorings and completely regular codes”, Des Codes Cryptogr, 61:3 (2011), 315–329  crossref  mathscinet  zmath  isi  elib
    4. A. A. Serov, “Otsenki ob'emov okrestnostei dvoichnykh kodov v terminakh ikh vesovykh spektrov”, Matem. vopr. kriptogr., 4:2 (2013), 17–42  mathnet  crossref
  • Проблемы передачи информации Problems of Information Transmission
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