Kurz S (2024)
Publication Language: English
Publication Status: In review
Publication Type: Unpublished / Preprint
Future Publication Type: Journal article
Publication year: 2024
We consider locally recoverable codes (LRCs) and aim to determine the smallest possible length n=n_q (k, d, r) of a linear [n, k, d]_q -code with locality r. For k ≤ 7 we exactly determine all values of n_2(k, d, 2) and for k ≤ 6 we exactly determine all values of n_2(k, d, 1). For the ternary field we also state a few numerical results. As a general result we prove that n_q(k, d, r) equals the Griesmer bound if the minimum Hamming distance d is sufficiently large and all other parameters are fixed.
APA:
Kurz, S. (2024). Bounds on the minimum distance of locally recoverable codes. (Unpublished, In review).
MLA:
Kurz, Sascha. Bounds on the minimum distance of locally recoverable codes. Unpublished, In review. 2024.
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