Exponential sums and constrained error-correcting codes
We present a number of new families of k-ary dc-constrained errorcorrecting codes with distance d > (k − 1)n/k − α1(n) √n and running digital sum ≅ α2(n) √n, where α1 and α2 are slowly growing functions in the code length n. We show also that constructed codes are comma-free and detect synchronization errors even at high rate of additive errors. To prove these properties of constructed codes, we apply some well-known inequalities for incomplete sums of characters of polynomials.
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