add "long full recoding" test (dragoon/komodo!147)
this will - recode for $\#steps \in [10, 20, 100]$ - at $t = 0$, $k$ random shards among the $n$ encoded will be selected at random - at $t \geq 1$, all $k$ shards will be used to recode $k$ brand new shards - make sure the last set of $k$ shards recoded $\#steps$ together can decode the data ## example with $(k, n) = (3, 5)$ and $\#steps = 3$ - $(s_i)_{1 \leq i \leq k}$ are the $k$ source shards - $(e_j)_{1 \leq j \leq n}$ are the $n$ encoded shards - $(m_i)_{1 \leq i \leq k}$ are the $k$ randomly selected shards - $(n_i)_{1 \leq i \leq k}$ are the shards after step $1$ - $(o_i)_{1 \leq i \leq k}$ are the shards after step $2$ - $(p_i)_{1 \leq i \leq k}$ are the shards after step $3$ - the $(p_i)_{1 \leq i \leq k}$ will be used for decoding ```mermaid graph TD; s1 --> e1; s1 --> e2; s1 --> e3; s1 --> e4; s1 --> e5; s2 --> e1; s2 --> e2; s2 --> e3; s2 --> e4; s2 --> e5; s3 --> e1; s3 --> e2; s3 --> e3; s3 --> e4; s3 --> e5; e1 --> m1; e3 --> m2; e4 --> m3; m1 --> n1; m1 --> n2; m1 --> n3; m2 --> n1; m2 --> n2; m2 --> n3; m3 --> n1; m3 --> n2; m3 --> n3; n1 --> o1; n1 --> o2; n1 --> o3; n2 --> o1; n2 --> o2; n2 --> o3; n3 --> o1; n3 --> o2; n3 --> o3; o1 --> p1; o1 --> p2; o1 --> p3; o2 --> p1; o2 --> p2; o2 --> p3; o3 --> p1; o3 --> p2; o3 --> p3; ```
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