ue of j; therefore, the code C is called a cyclic code. A bound on periodic cross-correlation magnitude for the 1 sequence set can be rewrit- ten in terms of Hamming distance for the corresponding cyclic code over GF(2), as (5.243) whence, (5.244) for all j, k, and T. Thus, the design of a set of J, period N, binary, roots-of- unity sequences to have small correlation, is equivalent to the design of a cyclic error-control code C containing NJ words of length N with the Hamming distance between all pairs of code words close to N/2. This link with error-control coding makes many of the design techniques in the well- developed theory of coding available for DS-SSMA signal design. Two well-known SSMA signal designs, namely Gold sequences [35], [36] and the small set of Kasami sequences [30], [31], are a direct result of design techniques for cyclic error-control codes. The Kasami sequences are among several known sets of sequences which nearly meet the Welch bound on Pmax, including bent sequences [32], and the prime-period group-character sequences [33]. The Kasami and bent sequence designs are both binary and possess identical numbers, periods, and periodic correlation properties, but the bent sequences have considerably longer linear span. The group- character sequences are non-binary but each design contains one binary sequence, namely the quadratic residue (or Legendre) sequence (e.g., see [12], Chapter 3, Section 5.6). Gold sequence sets, although not meeting the Welch bound, are larger than the Kasami and bent sets, and achieve a more restricted bound of Sidelnikov [39], which states that for any N binary (+1) sequences of period N, Pmax>(2N-2)12. (5.245) The Gold, Kasami, and bent designs will be developed later in this section. 5.7.3 Cross-Correlation of Binary M-Sequences It is clear from Table 5.6 that for reasonable register lengths, e.g., 20 to 30 stages, there exist large numbers of cyclically distinct m-sequences. Therefore, it is reasonable to determine whether or not several m-sequences can be used P