Abstract
We construct a family of linear maximally recoverable codes with locality r and dimension \(r+1.\) For codes of length n with \(r\approx n^\alpha , 0\le \alpha \le 1\) the code alphabet is of the order \(n^{1+3\alpha },\) which improves upon the previously known constructions of maximally recoverable codes.
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Notes
We use standard asymptotic notation: for functions \(f(n), g(n), n\in {\mathbb {N}}\) we write \(f(n)=O(g(n))\) if \(f(n)\le C g(n)\) for some constant C starting with some n; \(f(n)=\Omega (g(n))\) if \(f(n)\ge cg(n)\) starting with some n, and \(f(n)=\Theta (g(n))\) if both \(f(n)=O(g(n))\) and \(g(n)=O(f(n))\).
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Acknowledgements
Alexander Barg was partially supported by NSF-BSF grant CCF2110113 and NSF grant CCF2104489. Itzhak Tamo was supported by the European Research Council (ERC Grant No. 852953) and by the Israel Science Foundation (ISF Grant No. 1030/15).
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Communicated by V. A. Zinoviev.
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Barg, A., Chen, Z. & Tamo, I. A construction of maximally recoverable codes. Des. Codes Cryptogr. 90, 939–945 (2022). https://doi.org/10.1007/s10623-022-01020-8
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DOI: https://doi.org/10.1007/s10623-022-01020-8