Parity check Erasure code

parity check special case n = k + 1. set of k values



{

v

i



}

1
≤
i
≤
k




{\displaystyle \{v_{i}\}_{1\leq i\leq k}}

, checksum computed , appended k source values:

v

k
+
1


=
−

∑

i
=
1


k



v

i


.


{\displaystyle v_{k+1}=-\sum _{i=1}^{k}v_{i}.}

the set of k + 1 values



{

v

i



}

1
≤
i
≤
k
+
1




{\displaystyle \{v_{i}\}_{1\leq i\leq k+1}}

consistent regard checksum. if 1 of these values,




v

e




{\displaystyle v_{e}}

, erased, can recovered summing remaining variables:

v

e


=
−

∑

i
=
1
,
i
≠
e


k
+
1



v

i


.


{\displaystyle v_{e}=-\sum _{i=1,i\neq e}^{k+1}v_{i}.}