An m-ary balanced code with r check digits and k information digits is a code over the alphabet ℤm = {0, 1,...,m–1} of length n = k + r and cardinality mk such that each codeword is balanced; that is, the real sum of its components (or weight) is equal to ⌊(m – 1)n/2⌋. This paper contains new efficient methods to design m-ary balanced codes which improve the constructions found in the literature, for all alphabet size m ⩾ 2. To design such codes, the information words which are close to be balanced are encoded using single maps obtained by a new generalization of Knuth's complementation method to the m-ary alphabet that we introduce in this paper. Whereas, the remaining information words are compressed via suitable m-ary uniquely decodable variable length codes and then balanced using the saved space. For any m ⩾ 2, infinite families of m-ary balanced codes are given with r check digits and k ⩽ [1/(1 – 2α)][(mr – 1)/(m – 1)] – c1(m, α) r – c2(m, α) information digits, where α ∈ [0, 1/2) can be chosen arbitrarily close to 1/2. The codes can be implemented with O(mk logm k) m-ary digit operations and O(m + k) memory elements to store m-ary digits.
