The invention is a method and apparatus for generating a primary pseudorandom bit sequence consisting of a plurality of contiguous P subsequences. Each P subsequence consists of a start sequence of predetermined length followed by a sequence of trailing bits. The method comprises three steps. The first step consists of deriving a feedback bit from each generating sequence in a P subsequence in accordance with a specified rule where a generating sequence is any sequence of contiguous bits in the P subsequence having the same length as the start sequence. The bit that follows a generating sequence is called the trailing bit for that generating sequence. The second step of the method consists of determining a sequence of one or more modifier bits to be used in modifying the P subsequence. The third step of the method consists of modifying the P subsequence utilizing the one or more modifier bits.