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Non-existence of a ternary constant weight $(16,5,15;2048)$ diameter perfect code
Nearly perfect sequences with arbitrary out-of-phase autocorrelation
1. | Department of Mathematics, Hacettepe University, Beytepe, 06800, Ankara |
References:
[1] |
T. Beth, D. Jungnickel and H. Lenz, Design Theory, 2nd edition, Cambridge Univ. Press, 1999. |
[2] |
B. W. Brock, Hermitian congruence and the existence and completion of generalized Hadamard matrices, J. Combin. Theory Ser. A, 49 (1988), 233-261.
doi: 10.1016/0097-3165(88)90054-4. |
[3] |
Y. M. Chee, Y. Tan and Y. Zhou, Almost $p$-ary perfect sequences, in Sequences and their Applications - SETA 2010, Springer, Berlin, 2010, 399-415.
doi: 10.1007/978-3-642-15874-2_34. |
[4] |
T. Helleseth and P. V. Kumar, Sequences with low correlation,, in Handbook of Coding Theory, ().
|
[5] |
D. Jungnickel and A. Pott, Perfect and almost perfect sequences, Discrete Appl. Math., 95 (1999), 331-359.
doi: 10.1016/S0166-218X(99)00085-2. |
[6] |
S. L. Ma and W. S. Ng, On non-existence of perfect and nearly perfect sequences, Int. J. Inf. Coding Theory, 1 (2009), 15-38.
doi: 10.1504/IJICOT.2009.024045. |
[7] |
S. L. Ma and A. Pott, Relative difference sets, planar functions, and generalized Hadamard matrices, J. Algebra, 175 (1995), 505-525.
doi: 10.1006/jabr.1995.1198. |
[8] |
S. L. Ma and B. Schmidt, On $(p^a,p,p^a,p^{a-1})$-relative difference sets, Des. Codes Crypt., 6 (1995), 57-71.
doi: 10.1007/BF01390771. |
[9] |
F. Özbudak, O. Yayla and C. C. Yíldírím, Nonexistence of certain almost $p$-ary perfect sequences, in Sequences and their Applications - SETA 2012, Springer, Heidelberg, 2012, 13-24.
doi: 10.1007/978-3-642-30615-0_2. |
[10] |
A. Pott, Finite Geometry and Character Theory, Springer-Verlag, Berlin, 1995. |
[11] |
R. J. Turyn, Character sums and difference sets, Pacific J. Math., 15 (1965), 319-346. |
[12] |
A. Winterhof, O. Yayla and V. Ziegler, Non-existence of some nearly perfect sequences, near Butson-Hadamard matrices, and near conference matrices,, preprint, ().
|
show all references
References:
[1] |
T. Beth, D. Jungnickel and H. Lenz, Design Theory, 2nd edition, Cambridge Univ. Press, 1999. |
[2] |
B. W. Brock, Hermitian congruence and the existence and completion of generalized Hadamard matrices, J. Combin. Theory Ser. A, 49 (1988), 233-261.
doi: 10.1016/0097-3165(88)90054-4. |
[3] |
Y. M. Chee, Y. Tan and Y. Zhou, Almost $p$-ary perfect sequences, in Sequences and their Applications - SETA 2010, Springer, Berlin, 2010, 399-415.
doi: 10.1007/978-3-642-15874-2_34. |
[4] |
T. Helleseth and P. V. Kumar, Sequences with low correlation,, in Handbook of Coding Theory, ().
|
[5] |
D. Jungnickel and A. Pott, Perfect and almost perfect sequences, Discrete Appl. Math., 95 (1999), 331-359.
doi: 10.1016/S0166-218X(99)00085-2. |
[6] |
S. L. Ma and W. S. Ng, On non-existence of perfect and nearly perfect sequences, Int. J. Inf. Coding Theory, 1 (2009), 15-38.
doi: 10.1504/IJICOT.2009.024045. |
[7] |
S. L. Ma and A. Pott, Relative difference sets, planar functions, and generalized Hadamard matrices, J. Algebra, 175 (1995), 505-525.
doi: 10.1006/jabr.1995.1198. |
[8] |
S. L. Ma and B. Schmidt, On $(p^a,p,p^a,p^{a-1})$-relative difference sets, Des. Codes Crypt., 6 (1995), 57-71.
doi: 10.1007/BF01390771. |
[9] |
F. Özbudak, O. Yayla and C. C. Yíldírím, Nonexistence of certain almost $p$-ary perfect sequences, in Sequences and their Applications - SETA 2012, Springer, Heidelberg, 2012, 13-24.
doi: 10.1007/978-3-642-30615-0_2. |
[10] |
A. Pott, Finite Geometry and Character Theory, Springer-Verlag, Berlin, 1995. |
[11] |
R. J. Turyn, Character sums and difference sets, Pacific J. Math., 15 (1965), 319-346. |
[12] |
A. Winterhof, O. Yayla and V. Ziegler, Non-existence of some nearly perfect sequences, near Butson-Hadamard matrices, and near conference matrices,, preprint, ().
|
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