The authors consider the construction of balanced error-correcting codes with distance close to half of the block length and bounded running digital sum. Use of these codes in cascade constructions allows derivation of a number of classes of DC-constrained codes of various lengths. The mathematical framework underlying the code construction is the theory of (incomplete) exponential sums. Essentially, the authors consider a class of codes formed by values of Legendre symbols of polynomials of bounded degree on the set of residues modulo a prime. In particular, taking linear polynomials, they obtain the Hadamard codes. Applying well-known estimates of the exponential sums, they compute the code parameters and prove that the proposed codes are in fact DC constrained.
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