Weight enumerators of codes derived from polynomial product algorithms Original Research Article

Let Z(u), Y(u) be polynomials with respective degrees k, d and coefficients {z sub i}, {y sub j}. Then each coefficient in the product Y(u)Z(u) is a sum of certain bilinear terms (z sub i)(y sub j). If there exist n bilinear forms to span these sums, there is a linear error-correcting code of length n, dimension k and minimum distance d. Such codes can be nested so as to provide a natural system for adapting to the intensity of interference. We determine the weight enumerators for a class of these codes.