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New bounds on the minimum distance of cyclic codes
School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371 |
Two bounds on the minimum distance of cyclic codes are proposed. The first one generalizes the Roos bound by embedding the given cyclic code into a cyclic product code. The second bound also uses a second cyclic code, namely the non-zero-locator code, but is not directly related to cyclic product codes and it generalizes a special case of the Roos bound.
References:
| [1] |
R. C. Bose and D. K. R. Chaudhuri,
On a class of error correcting binary group code, Information and Control, 3 (1960), 68-79.
doi: 10.1016/S0019-9958(60)90287-4. |
| [2] |
H. O. Burton and E. J. Weldon,
Cyclic product codes, IEEE Trans. Information Theory, 11 (1965), 433-439.
doi: 10.1109/tit.1965.1053802. |
| [3] |
C. Hartmann and K. Tzeng,
Generalizations of the BCH bound, Information and Control, 20 (1972), 489-498.
doi: 10.1016/S0019-9958(72)90887-X. |
| [4] |
A. Hocquenghem,
Codes correcteurs d'erreurs, Chiffres, 2 (1959), 147-156.
|
| [5] |
S. Lin and E. J. Weldon,
Further results on cyclic product codes, IEEE Trans. Information Theory, 16 (1970), 452-459.
doi: 10.1109/tit.1970.1054491. |
| [6] |
C. Roos,
A generalization of the BCH bound for cyclic codes, including the Hartmann-Tzeng bound, J. Combin. Theory Ser. A, 33 (1982), 229-232.
doi: 10.1016/0097-3165(82)90014-0. |
| [7] |
C. Roos,
A new lower bound for the minimum distance of a cyclic code, IEEE Trans. Inform. Theory, 29 (1983), 330-332.
doi: 10.1109/TIT.1983.1056672. |
| [8] |
A. Zeh and S. V. Bezzateev,
A new bound on the minimum distance of cyclic codes using small-minimum-distance cyclic codes, Des. Codes Cryptogr., 71 (2014), 229-246.
doi: 10.1007/s10623-012-9721-3. |
| [9] |
A. Zeh, A. Wachter-Zeh, M. Gadouleau and S. V. Bezzateev, Generalizing bounds on the minimum distance of cyclic codes using cyclic product codes, Proc. IEEE ISIT, Istanbul, Turkey, 2013,126–130.
doi: 10.1109/ISIT.2013.6620201. |
show all references
References:
| [1] |
R. C. Bose and D. K. R. Chaudhuri,
On a class of error correcting binary group code, Information and Control, 3 (1960), 68-79.
doi: 10.1016/S0019-9958(60)90287-4. |
| [2] |
H. O. Burton and E. J. Weldon,
Cyclic product codes, IEEE Trans. Information Theory, 11 (1965), 433-439.
doi: 10.1109/tit.1965.1053802. |
| [3] |
C. Hartmann and K. Tzeng,
Generalizations of the BCH bound, Information and Control, 20 (1972), 489-498.
doi: 10.1016/S0019-9958(72)90887-X. |
| [4] |
A. Hocquenghem,
Codes correcteurs d'erreurs, Chiffres, 2 (1959), 147-156.
|
| [5] |
S. Lin and E. J. Weldon,
Further results on cyclic product codes, IEEE Trans. Information Theory, 16 (1970), 452-459.
doi: 10.1109/tit.1970.1054491. |
| [6] |
C. Roos,
A generalization of the BCH bound for cyclic codes, including the Hartmann-Tzeng bound, J. Combin. Theory Ser. A, 33 (1982), 229-232.
doi: 10.1016/0097-3165(82)90014-0. |
| [7] |
C. Roos,
A new lower bound for the minimum distance of a cyclic code, IEEE Trans. Inform. Theory, 29 (1983), 330-332.
doi: 10.1109/TIT.1983.1056672. |
| [8] |
A. Zeh and S. V. Bezzateev,
A new bound on the minimum distance of cyclic codes using small-minimum-distance cyclic codes, Des. Codes Cryptogr., 71 (2014), 229-246.
doi: 10.1007/s10623-012-9721-3. |
| [9] |
A. Zeh, A. Wachter-Zeh, M. Gadouleau and S. V. Bezzateev, Generalizing bounds on the minimum distance of cyclic codes using cyclic product codes, Proc. IEEE ISIT, Istanbul, Turkey, 2013,126–130.
doi: 10.1109/ISIT.2013.6620201. |
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