Locally recoverable code: Difference between revisions

Revision as of 00:57, 7 December 2023

Revision as of 00:58, 7 December 2023

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Then f is said to be (r, ''l'')-good if

::• f has degree r + 1,

::• there exist <math>A_{1}</math> , . . . ,<math>A_{l}</math> distinct subsets of <math>F_{q}</math> such that

::::– for any i ∈ {1, . . ., l}, f (<math>A_{i}</math> ) = {<math>t_{i}</math>} for some ti ∈ <math>F_{q}</math> , i.e. f is constant on Ai ,

::::– #<math>A_{i}</math> = r + 1,

::::– <math>A_{i}</math> ∩ <math>A_{j}</math> = ∅ for any i ≠ j.

We say that {<math>A_{1}</math> , . . . , <math>A_{l}</math>} is a splitting covering for f .