A general formulation of error matrices (Corresp.)

A general definition of error metrics is given, based on a distance function
\mu(a, b)
for symbols of the code alphabet, and extended to entire codewords by a Lebesgue norm
L_{\alpha}
. It is shown that error metrics considered by Hamming, Lee, Shannon, and Stein are special cases, and a geometric interpretation of the "error spheres" for these metrics is presented.