On balanced codes over the m-th roots of unity, m=4

This paper completely solves the coding problem for balanced codes over Φ_m, when m = 4. In fact, it reduces the problem of designing efficient coding schemes for balanced codes over Φ₄ to the design of efficient balanced codes over Φ4 = {-1,+1}. In particular, the paper proposes efficient constructions for balanced codes over Φ₄ with k information digits and r=2log₄k -log₄s(k) + Θ(1), check digits, where s(k) is any function such that 1≤s(k)≤k. Such balanced codes can be implemented with T=O(klogk:+ ks(k)) digit operations, by storing A=O(k+s³(k)) memory digits. The paper also shows that the minimum redundancy for a balanced code over Φ₄ of length n is r_min ≈ Iog₄n+0.326.