Abstract
We obtain new bounds on the parameters and we give new constructions of linear error-block codes. We obtain a Gilbert–Varshamov type construction. Using our bounds and constructions we obtain some infinite families of optimal linear error-block codes over \(\mathbb{F}_2\). We also study the asymptotic of linear error-block codes. We define the real valued function α q,m,a (δ), which is an analog of the important real valued function α q (δ) in the asymptotic theory of classical linear error-correcting codes. We obtain both Gilbert–Varshamov and algebraic geometry type lower bounds on α q,m,a (δ). We compare these lower bounds in graphs.
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Communicated by: G. McGuire.
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Ling, S., Özbudak, F. Constructions and bounds on linear error-block codes. Des. Codes Cryptogr. 45, 297–316 (2007). https://doi.org/10.1007/s10623-007-9119-9
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DOI: https://doi.org/10.1007/s10623-007-9119-9
Keywords
- Linear error-block codes
- Gilbert–Varshamov type construction
- Optimal linear error-block codes
- Asymptotic of linear error-block codes
- Gilbert–Varshamov bound
- Algebraic geometry type bound