add an example to study the _recoding inbreeding_ phenomenon

this MR adds examples/inbreeding.rs which allows to do two things

• naive recoding: in order to generate a new random shard, we first k-decode the whole data and then 1-encode a single shard
• true recoding: to achieve the same goal, we directly k-recode shards into a new one

the scenario

regardless of the recoding strategy, the scenario is the same

1. data is split into k shards and n original shards are generated
2. for a given number of steps s, k shards are drawn randomly with replacement and we count the number of successful decoding, given a measure of the diversity, \delta = \frac{\#success}{\#attempts}
3. create a new recoded shard and add it to the n previous ones, i.e. n increases by one
4. repeat steps 2. and 3. as long as you want

results

examples/inbreeding.rs

@@ -112,7 +112,7 @@ fn measure_inbreeding<F: PrimeField>(
     nb_measurements: usize,
     rng: &mut impl RngCore,
 ) -> f64 {
-    let mut s: Vec<_> = shards.iter().cloned().collect();
+    let mut s: Vec<_> = shards.to_vec();
     let mut count = 0;
     for _ in 0..nb_measurements {
         // get any k of the shards
@@ -146,7 +146,7 @@ fn end_to_end<F: PrimeField>(
 
         // re-encode a new random shard
         let encoding_mat = Matrix::vandermonde_unchecked(&[F::rand(rng)], k);
-        let new_shard = fec::encode(&data, &encoding_mat)?.get(0).unwrap().clone();
+        let new_shard = fec::encode(&data, &encoding_mat)?.first().unwrap().clone();
         shards.push(new_shard);
     }
     eprintln!();