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.