Improved Information Set Decoding - Decoding Random Linear ...

Recap Binary Linear Codes
n
A binary linear code C is a k-dimensional subspace of F
●
Running time of decoding algorithms: T(n,k,d)
2
●
In
● Generator this talk: Analysis
matrix for random
G k
=
0 binary / 1 linear
C = { x t·G k
: x 2 F 2
}
codes with constant rate R=k/n
●
For n→∞, k and d are related via Gilbert-
n
n-k
n
● Parity Varshamov check matrix bound, thus
H = 0 / 1 C = { H·c = 0 : c 2 F 2
}
T(n,k,d) = T(n,k)
●
We compare algorithms by their complexity
·
y
d
Minimum coeffcient distance F(k), d i.e. = min c2C
{ wt(c) }
x
· ·
Such C is called binary T(n,k) [n,k,d] = O(2 code.
F(k)n )
n
IMPROVED INFORMATION SET DECODING ASIACRYPT 2011 | December 2011, Seoul