Strengthening the Gilbert–Varshamov bound
@article{Barg2000StrengtheningTG,
title={Strengthening the Gilbert–Varshamov bound},
author={A. Barg and S. Guritman and J. Simonis},
journal={Linear Algebra and its Applications},
year={2000},
volume={307},
pages={119-129}
}Abstract The paper discusses some ways to strengthen (nonasymptotically) the Gilbert–Varshamov bound for linear codes. The unifying idea is to study a certain graph constructed on vectors of low weight in the cosets of the code, which we call the Varshamov graph. Various simple estimates of the number of its connected components account for better lower bounds on the minimum distance of codes, some of them known in the literature.
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References
SHOWING 1-10 OF 15 REFERENCES
Improvement on Varshamov-Gilbert lower bound on minimum Hamming distance of linear codes
- Mathematics
- 1978
- 6
Some results on the existence of binary linear codes
- Mathematics, Computer Science
- IEEE Trans. Inf. Theory
- 1983
- 6
Algebraic-Geometric Codes (Translated from the Russian by the authors)
- Mathematics and its Applications (Soviet Series)
- 1991
Vladut, Algebraic-Geometric Codes (Translated from the Russian by the authors)
- Mathematics and its Applications (Soviet Series),
- 1991