Binary pulse compression codes

TL;DR: This analytical technique produced codes for lengths near 100 digits as good as, or better than, any previously known binary pulse compression codes in less than 15 minutes computer time.

Abstract: An analytical technique for generating good binary pulse compression codes is developed. The first step in constructing a code of a given length N is to divide all the residues modulo N and less than N into residue classes. A code digit a(i)=\pm 1 is assigned to all members, i , of certain of these classes and a(i)=-1 to N and all members, i , of the remaining classes. Many of these divisions resulted in difference sets and corresponding binary codes with single-level periodic code correlations. Other divisions resulted in two-level periodic code correlations. In order for a binary pulse compression code to have low autocorrelation sidelobes, its periodic correlation sidelobes must be low. Therefore, codes with low periodic correlations were sought. Good binary codes for lengths just above 100 digits down to lengths near 10 digits were found. Several of them are known to be optimum codes. When programmed on an IBM 7094 , this analytical technique produced codes for lengths near 100 digits as good as, or better than, any previously known binary pulse compression codes in less than 15 minutes computer time.