TY - GEN
T1 - Nonexistence of a kind of generalized perfect binary array
AU - Xiyong, Zhang
AU - Hua, Guo
AU - Wenbao, Han
PY - 2006
Y1 - 2006
N2 - Generalized perfect binary array(GPBA) is a useful tool in the construction of perfect binary arrays. By investigating the character values of corresponding relative difference sets, we obtain some nonexistence results of GPBAs. In particular, we show that no GPBA(2, 2, pn) of any type z exists for n = 1 and any odd prime p, or for any n and any odd prime p ≢ 1 (mod 8). For the case p = 2, there exists a GPBA(2, 2, 2n) of type z = (z1, z2, z3) if and only if z = (0, 0, 0) and n = 0, 2, 4, or 2 ≠ (0, 0, 0) with z3 = 0 and 0 ≤ n ≤ 5, with z3 = 1 and 0 ≤ n ≤ 3.
AB - Generalized perfect binary array(GPBA) is a useful tool in the construction of perfect binary arrays. By investigating the character values of corresponding relative difference sets, we obtain some nonexistence results of GPBAs. In particular, we show that no GPBA(2, 2, pn) of any type z exists for n = 1 and any odd prime p, or for any n and any odd prime p ≢ 1 (mod 8). For the case p = 2, there exists a GPBA(2, 2, 2n) of type z = (z1, z2, z3) if and only if z = (0, 0, 0) and n = 0, 2, 4, or 2 ≠ (0, 0, 0) with z3 = 0 and 0 ≤ n ≤ 5, with z3 = 1 and 0 ≤ n ≤ 3.
UR - https://www.scopus.com/pages/publications/33749674364
U2 - 10.1007/11863854_26
DO - 10.1007/11863854_26
M3 - 会议稿件
AN - SCOPUS:33749674364
SN - 3540445234
SN - 9783540445234
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 304
EP - 312
BT - Sequences and Their Applications, SETA 2006 - 4th International Conference, Proceedings
PB - Springer Verlag
T2 - 4th International Conference on Sequences and Their Applications, SETA 2006
Y2 - 24 September 2006 through 28 September 2006
ER -