Work Inside GF Five - Erasure Codes Rebuild a Missing Number

Erasure recovery starts with exact arithmetic in a tiny field.

highlighted = computed this step

Use a tiny field

This toy works in GF(5), so every result is reduced back into the field.

\text{field size}=5

The field values are 0, 1, 2, 3, and 4.

0\ldots4

If a calculation reaches 5, it wraps to 0 because we reduce modulo 5.

5\equiv0\pmod{5}

The table will only show field values. No decimal approximation is involved.

\text{exact field arithmetic}