A THEORETICAL STUDY OF COMPLEMENTARY BINARY CODE SEQUENCES AND A COMPUTER SEARCH FOR NEW KERNELS
Abstract:
Complementary binary sequences invented by M. J. E. Golay in an investigation of infra-red multi-slit spectrometry are investigated. The basic results obtained by Golay are formalized and new concepts and techniques are developed for examining the characteristics of these special binary codes. This work has developed new understanding of the structure and methods for the decomposition of complementary sequences. Complementary sequences have the property of an infinite correlation peak to ambiguity ratio when detected with a matched filter. These binary sequences should find much application as pseudo- random noise modulation signals for both radar and communications systems. Several invariant properties of complementary codes are proved through the use of the Hamming distance concept. Several computer searches for complementary sequences are described and the actual computer programs for the CDC 1604 are included.