Maximum-weight group codes for the balanced M -ary channel
Carl W. Helstrom · IEEE Transactions on Information Theory · 1960
The construction of(n, k)group alphabets is discussed for the balancedM-ary channel, whereMis the power of a prime. In this channel allMdigits are equally likely to be in error, and an incorrect digit is equally likely to be any digit besides the one sent. The alphabets are formed by takingncolumns of the modular representation table of the Abelian group ofk-tuples of elements from the Galois fieldGF(M)under digitwise addition. The formation and properties of that table are described. Attention is focused on alphabets in which all letters except then-tuple of O's have the maximum number of non-null elements. Tables of such alphabets are given forM = 2, k = 2, 3, 4; M = 3, k = 2, 3; andM = 4, k = 2, 3.