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Problemy Peredachi Informatsii, 2004, Volume 40, Issue 2, Pages 19–36
(Mi ppi130)
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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 $n$.
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
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https://www.mathnet.ru/eng/ppi130 https://www.mathnet.ru/eng/ppi/v40/i2/p19
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Abstract page: | 407 | Full-text PDF : | 101 | References: | 40 | First page: | 2 |
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