Abstract
We present a number of new families of k-ary dc-constrained errorcorrecting codes with distance d > (k − 1)n/k − α 1 (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.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
R.P.Bambah,D.D.Joshi, and I.S.Luthar. Some lower bounds on the number of code points in a minimum distance binary codes I,II. Inform. and Contr., 4,4 (December 1961), 313–323.
L.A.Bassalygo. On separable comma-free codes. Problemy Peredachi Inform., 2,4 (1966), 78–79, and Probl. Inform. Trans. 2 (1966), 52–53.
A.M.Barg and S.N.Litsyn DC-constrained codes from Hadamard matrices. IEEE Trans. Inform. Theory, 37, 3, Pt.2 (May 1991), 801–807.
E.R.Berlecamp. Algebraic Coding Theory. McGraw Hill, N.Y. et al., 1968.
S.Golomb, W.Gordon, and L.Welch. Comma-free codes. Canad. J. Math., 10, 2 (1958), 202–209.
V.I.Levenstein. Bounds for codes that provide error correction and synchronization. Problemy Peredachi Inform.,5,2 (1969), 3–13, and Probl. Inform. Trans. 5 (1969).
V.I.Levenstein. One method of constructing quasilinear codes providing synchronization in the presence of errors. Problemy Peredachi Inform., 7,3 (1971), 30–40, and Probl. Inform. Trans, 7 (1971), 215–227.
F.J.MacWilliams and N.J.A.Sloane. The Theory of Error-Correcting Codes. North-Holland, Amsterdam, 1977.
V.M.Sidel'nikov. Some k-valued pseudo-random sequences and nearly equidistant codes. Problemy Peredachi Inform., 5,1 (1967),16–22, and Probl. Inform. Trans., 5 (1969), 12–16.
I.M.Vinogradov. Elements of Number Theory. 9th ed., Moscow, 1981, in Russian.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Barg, A. (1992). Exponential sums and constrained error-correcting codes. In: Cohen, G., Lobstein, A., Zémor, G., Litsyn, S. (eds) Algebraic Coding. Algebraic Coding 1991. Lecture Notes in Computer Science, vol 573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0034336
Download citation
DOI: https://doi.org/10.1007/BFb0034336
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55130-0
Online ISBN: 978-3-540-46739-7
eBook Packages: Springer Book Archive