A new approach to error-correcting codes

A correspondence between linear
(n,k,d)
codes and algorithms for computing a system
\psi
of
k
bilinear forms is established under which the codelength
n
is equal to the multiplicative complexity of the algorithm for computing
\psi
, and the code distance
d
is underbounded by the minimum number of multiplications required to compute any linear combination of the
k
forms in
\psi
. This hitherto unexplored approach to linear codes holds promise of a better understanding of the structure of existing codes as well as for methods of constructing new codes with prescribed rate and distance.