Abstract
The exact number of nonperiodic cyclic equivalence classes (NCEC) in cyclic code is determined. By NCEC, several algebraic constructions of cyclically permutable (CP) codes are given in this paper. These constructions can yield good (large size) CP codes. Furthermore, we present detailed discussions for some well known cyclic codes. By using the above CP codes, we can obtain good (large size) binary constant weight CP codes and protocol-sequence sets for collision channel without feedback according the methods in [1].
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N.Q. A, L. Györfi, and J.L. Massey. “Constructions of binary constant-weight cyclic codes”, IEEE Trans. Inform. Theory, 1992, 38(3): 940–949.
H. Song, I. Reed, S. Golomb. “On the nonperiodic cyclic equivalence classes of Reed-Solomon codes,” IEEE Trans. on Inform. Theory, 1993, 39(4): 1431–1434.
L. Györfi, I. Vajda. “Constructions of protocol sequence for multiple access collision channel without feedback,” IEEE Trans. on Inform. Theory, 1993, 39(5): 1762–1765.
N.Q. A, “Families of sequences with optimal generalized Hamming correlation properties,” Problems of Control and Information Theory, 1988, 17(3): 117–123.
E.N. Gilbert. “Cyclically permutable error-correcting codes,” IEEE Trans. on Inform. Theory, vol. 9, pp. 175–182, July 1963.
E.R. Berlekamp and J. Justesen. “Some long cyclic linear binary codes are not so bad,” IEEE Trans. on Inform. Theory, vol. 20, pp. 351–356, May 1974.
C. Kościelny. “Constructing a better cyclic code than cyclic Reed-Solomon code,” IEEE Trans. on Inform. theory, 1995, 41(4): 1191–1194.
A.W. Lam and D.V. Sarwate. “Time-hopping and frequency-hopping multipleacces packet communications,” IEEE Trans. on Commun., 1990, 38(6): 875–888.
I. Vajda and G. Einarsson. “Code acquisition for a frequency-hopping system,” IEEE Trans. Commun., 1987, 35(5): 566–568.
R. Gagliardi, J. Robbins and H. Taylor. “Acquisition sequence in PPM communications,” IEEE Trans. on Inform. Theory, 1987, 33(5): 738–744.
R. Blahut. Theory and Practice of Error Control Codes, Addison-Wesley, 1987.
D.M. Burton. Elementary Number theory, Boston, MA: Allyn and Bacon Inc., 1980.
Z.X. Wan. Algebra and Coding (in Chinese), Beijing: Science Press, 1984.
S. Roman. Coding and Information Theory, Berlin: Springer-Verlag, 1992.
H.F. Mattson and G. Solomon. “A new treatment of Bose-Chaudhuri codes,” J. SIAM, 1961, vol. 9, pp. 654–669. reprinted in Key Papers in the Development of Coding Theory, E. R. Berlekamp, ed., 82–86, New York: IEEE Press, 1974.
F.J. MacWilliams and N.J.A. Sloane. The Theory of Error-Correcting Codes, New York: North-Holland, 1977.
B. Elspas. “The Theory of Autonomous Linear Sequential Networks,” IRE Transactions on Circuit Theory, vol. CT-6, pp. 45–60, March 1959. reprinted in Linear Sequential Switching Circuits: Selected Technical Papers, W. Kautz, ed., 21–61, San Francisco, Holden-Day, 1965.
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© 1997 Springer-Verlag Berlin Heidelberg
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Xia, S., Fu, F. (1997). Nonperiodic cyclic equivalence classes of cyclic codes and algebraic constructions of cyclically permutable codes. In: Mora, T., Mattson, H. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1997. Lecture Notes in Computer Science, vol 1255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63163-1_27
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DOI: https://doi.org/10.1007/3-540-63163-1_27
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