A Line Makes Shards - Erasure Codes Rebuild a Missing Number

A tiny polynomial turns x positions into shard values.

highlighted = computed this step

Pin the line

The shard rule is f of x equals 2 plus 3 times x, all modulo 5.

f(x)=2+3x\pmod{5}

At x equals 0, the shard value is the intercept 2.

f(0)=2

Each step in x adds slope 3 before the modulo wrap.

\text{slope}=3

A tiny line creates several shard numbers. Later, two kept points can rebuild the same line.

\text{two points rebuild a line}