Locally recoverable code: Difference between revisions

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== Tamo-Barg Codes ==
Let f ∈ Fq [X]F_{q}</math> be a polynomial and let ''l'' be a positive integer.
Then f is said to be (r, ''l'')-good if
• f has degree r + 1,
• there exist A A_{1}</math> , . . . A�A_{''l''}</math> distinct subsets of Fq such that
– for any i ∈ {1, . . . ,''l''}, f (A A_{i }</math>) = {t t_{i }</math>} for some tit_{i}</math>F F_{q}</math> , i.e. f is constant on Ai ,
– #A A_{i}</math> = r + 1,
on Ai ,
AiA_{i}</math>A A_{j}</math> = ∅ for any i ≠ j.
– #A i = r + 1,
We say that {A1 A_{1}</math>, . . . , A � A_{''l''}</math>} is a splitting covering for f
– Ai ∩ A j = ∅ for any i ≠ j.
We say that {A1 , . . . , A � } is a splitting covering for f