A new approach to error-correcting codes
Abraham Lempel, Shmuel Winograd · IEEE Transactions on Information Theory · 1977
A correspondence between linear(n,k,d)codes and algorithms for computing a system\psiofkbilinear forms is established under which the codelengthnis equal to the multiplicative complexity of the algorithm for computing\psi, and the code distancedis underbounded by the minimum number of multiplications required to compute any linear combination of thekforms 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.