Abstract
Binary asymmetric error-correcting codes play an important role in communication systems modeled by the binary symmetric channel. In this paper, we study binary asymmetric error-correcting codes and give a general construction for binary asymmetric error-correcting codes. The construction makes an improvement on the lower bounds of binary asymmetric error-correcting codes in [17].
This research work is supported by the National Natural Science Foundation of China (Nos. 61171082, 10990011, 60872025).
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References
Abdel-Ghaffar, K.A.S., Ferreira, H.C.: Systematic encoding of the Varshamov-Tenengol’ts codes and the Constantin-Rao codes. IEEE Trans. Inform. Theory 44, 340–345 (1998)
Al-Bassam, S., Bose, B.: Asymmetric/unidirectional error correcting and detecting codes. IEEE Trans. Computers C-43, 590–597 (1994)
Al-Bassam, S., Venkatesan, R., Al-Muhammadi, S.: New single asymmetric error-correcting codes. IEEE Trans. Inform. Theory 43, 1619–1623 (1997)
Al-Bassam, S., Al-Muhammadi, S.: A single asymmetric error-correcting code with 213 codewords of dimension 17. IEEE Trans. Inform. Theory 46, 269–271 (2000)
Berger, J.M.: A note on error detection codes for asymmetric channels. Inform. Contr. 4, 68–73 (1961)
Blaum, M.: Codes for Detecting and Correcting Unidirectional Errors. IEEE Computer Society Press, Los Alamitos (1993)
Borden, J.M.: Optimal asymmetric error detecting codes. Inform. Contr. 53, 66–73 (1982)
Borden, J.M.: A low-rate bound for asymmetric error-correcting codes. IEEE Trans. Inform. Theory 29, 600–602 (1983)
Bose, B., Cunningham, S.: Asymmetric error correcting codes. In: Capocelli, R., De Santis, A., Vaccaro, U. (eds.) Sequences II: Methods in Communication, Security, and Computer Science, pp. 24–35. Springer, Heidelberg (1993)
Bose, B., Al-Bassam, S.: On systematic single asymmetric error-correcting codes. IEEE Trans. Inform. Theory 46, 669–672 (2000)
Constantin, S.D., Rao, T.R.N.: On the theory of binary asymmetric error-correcting codes. Inform. Contr. 40, 20–36 (1979)
Delsarte, P., Piret, P.: Spectral enumerators for certain additive-error-correcting codes over integer alphabets. Inform. Contr. 48, 193–210 (1981)
Delsarte, P., Piret, P.: Bounds and constructions for binary asymmetric error-correcting codes. IEEE Trans. Inform. Theory 27, 125–128 (1981)
Etzion, T.: Lower bounds for asymmetric and unidirectional codes. IEEE Trans. Inform. Theory 37, 1696–1704 (1991)
Fang, G., van Tilborg, H.C.A.: Bounds and constructions of asymmetric or unidirectional error-correcting codes. Appl. Algebra Engrg. Comm. Comput. 3(4), 269–300 (1992)
Freiman, C.V.: Optimal error detection codes for completely asymmetric binary channels. Inform. Contr. 5, 64–71 (1962)
Fu, F.W., Ling, S., Xing, C.P.: New lower bounds and constructions for binary codes correcting asymmetric errors. IEEE Trans. Inform. Theory 49(12), 3294–3299 (2003)
Helleseth, T., Kløve, T.: On group-theoretic codes for asymmetric channels. Inform. Contr. 49, 1–9 (1981)
Kim, H., Freiman, C.: Single error-correcting codes for asymmetric binary channels. IRE Trans. Inform. Theory IT-5, 62–66 (1959)
Kløve, T.: Error correcting codes for the asymmetric channel. Rep. 18-09-07-81, Dept. Mathematics, University of Bergen (1981) (revised in 1983 and updated in 1995)
Kløve, T.: Upper bounds on codes correcting asymmetric errors. IEEE Trans. Inform. Theory 27, 128–131 (1981)
Kløve, T.: On Robinson’s coding problem. IEEE Trans. Inform. Theory 29, 450–454 (1983)
McEliece, R.J.: Comment on ‘A class of codes for asymmetric channels and a problem from the additive theory of numbers’. IEEE Trans. Inform. Theory 19, 137 (1973)
McEliece, R.J., Rodemich, E.R.: The Constantin-Rao construction for asymmetric error-correcting-codes. Inform. Contr. 44, 187–196 (1980)
Rao, T.R.N., Chawla, A.S.: Asymmetric error codes for some LSI semi-conductor memories. In: Proc. Ann. Southeastern Symp. Syst. Theory, pp. 170–171 (1975)
Rao, T.R.N., Fujiwara, E.: Error-Control Coding for Computer Systems. Prentice-Hall Inc., Englewood Cliffs (1989)
Robinson, J.P.: An asymmetric error-correcting ternary code. IEEE Trans. Inform. Theory 24, 258–261 (1978)
Saitoh, Y., Yamaguchi, K., Imai, H.: Some new binary codes correcting asymmetric/unidirectional errors. IEEE Trans. Inform. Theory 36, 645–647 (1990)
Serre, J.P.: Nombre de points de courbes algébriques sur \(\mathbb{F}\) q . in Sém. Théorie Nombres Bordeux 22, 1–8 (1982)
Shiozaki, A.: Construction for binary asymmetric error-correcting codes. IEEE Trans. Inform. Theory 28, 787–789 (1982)
Stanley, R.P., Yoder, M.F.: A study of Varshamov codes for asymmetric channels. Jet Prop. Lab. Tech. Rep. 32-1526 14, 117–122 (1973)
Stichtenoth, H.: Algebraic function fields and codes. Springer, Berlin (1993)
Varshamov, R.R.: A class of codes for asymmetric channels and a problem from the additive theory of numbers. IEEE Trans. Inform. Theory 19, 92–95 (1973)
Varshamov, R.R., Tenenholtz, G.M.: Correction code for single asymmetric error. Automat. Remote Contr. 26, 286–290 (1965)
Waterhouse, W.C.: Abelian varieties over finite fields. Ann. Sci. Ecole Norm. Supp. 2(4), 521–560 (1969)
Weber, J., De Vroedt, C., Boekee, D.: New upper bounds on the size of codes correcting asymmetric errors. IEEE Trans. Inform. Theory 33, 434–437 (1987)
Weber, J., De Vroedt, C., Boekee, D.: Bounds and constructions for binary codes of length less than 24 and asymmetric distance less than 6. IEEE Trans. Inform. Theory 34, 1321–1331 (1988)
Xing, C.: Constructions of codes from residue rings of polynomials. IEEE Trans. Inform. Theory 48(11), 2995–2997 (2002)
Xing, C., Ling, J.: A construction of binary constant-weight codes from algebraic curves over finite fields. IEEE Trans. Inform. Theory 51(10), 3674–3678 (2005)
Zhang, Z., Xia, X.: New lower bounds for binary codes of asymmetric distance two. IEEE Trans. Inform. Theory 38, 1592–1597 (1992)
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Zhang, J., Fu, FW. (2012). Constructions for Binary Codes Correcting Asymmetric Errors from Function Fields. In: Agrawal, M., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2012. Lecture Notes in Computer Science, vol 7287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29952-0_30
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DOI: https://doi.org/10.1007/978-3-642-29952-0_30
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