WEIGHT DISTRIBUTIONS OF LINEAR CODES AND THE GLEASON-PIERCE THEOREM

The Gleason-Pierce theorem characterizes those fields for which formal ly self-dual divisible codes can exist. The ideas underlying the proof of the theorem yield necessary conditions on whether a solution to th e MacWilliams identity can be the weight distribution of a linear code . Consequences of this result are an algebraic proof of the non-existe nce of an [16, 8, 6] f.s.d. binary even code, restrictions on distribu tion of cosets of codes, and occasional sharpening of upper bounds on the covering radius. (C) 1994 Academic Press, Inc.