周期互补序列的压缩及其应用
Compression of Periodic Complementary Sequences and Applications
摘要：
长度为v的复序列的集合是互补的，如果它们的周期性自相关函数值在所有非零移位处的和是恒定的。对于复序列A=[a_0，a_1，.，a_{v-1} ]定义长度为d的m压缩序列A^{（d）}，其项是和a_i + a_{i+d} +. + a_{i+(m-1)d}。我们证明了互补序列集合的m-压缩也是互补的。该压缩过程可用来简化复合长度互补{+1，-1}-序列的构造。特别地，我们构造了几个补充差集（v;r，s;lambda），其中v是偶数，lambda=（r+s）-v/2，在这里首次给出。有15个归一化参数集（v;r，s;lambda），其中v <= 50，存在问题是开放的。我们解决了所有这些案件，除了一个。
英文摘要：
A collection of complex sequences of length v is complementary if the sum of their periodic autocorrelation function values at all non-zero shifts is constant. For a complex sequence A=[a_0,a_1,...,a_{v-1}] of length v=dm we define the m-compressed sequence A^{(d)} of length d whose terms are the sums a_i + a_{i+d} + ... + a_{i+(m-1)d}. We prove that the m-compression of a complementary collection of sequences is also complementary. The compression procedure can be used to simplify the construction of complementary {+1,-1}-sequences of composite length. In particular, we construct several supplementary difference sets (v;r,s;lambda) with v even and lambda=(r+s)-v/2, given here for the first time. There are 15 normalized parameter sets (v;r,s;lambda) with v <= 50 for which the existence question was open. We resolve all but one of these cases.
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