Research partially supported by NSA Grant MDA 904-91-H-0003
We thank G. Kabatyanski for pointing out Levenshtein's results, reference 3. This paper contains the first proof of the linearity of lexicodes. It also states, but does not prove, that B-greedy codes are linear.
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References
R. A. Brualdi and V. Pless, Greedy codes, preprint.
J. H. Conway and N. J. A. Sloane, Lexicographic codes; Error-correcting codes from game theory IEEE Trans. Inform. Theory, vol IT-32, 1986, 337–348.
V. I. Levenshtein, A class of systematic codes. Dokl. Akad. Nauk SSSR131 (1960), 1011–1014 (Russian); translated as Soviet Math. Dokl.1, 368–371.
T. Verhoeff, An updated table for minimum-distance bounds for binary linear codes, IEEE Trans. Inform. Theory, vol IT-33, 1987, 665–680.
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© 1992 Springer-Verlag Berlin Heidelberg
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Pless, V. (1992). Remarks on greedy codes. In: Cohen, G., Lobstein, A., Zémor, G., Litsyn, S. (eds) Algebraic Coding. Algebraic Coding 1991. Lecture Notes in Computer Science, vol 573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0034341
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DOI: https://doi.org/10.1007/BFb0034341
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