Kasami code

Kasami code

Kasami sequences are binary sequences of length 2N where N is an even integer. Kasami sequences have good cross-correlation values approaching the Welch lower bound. There are two classes of Kasami sequences - the small set and the large set.

The small set

The process of generating a Kasami sequence starts by generating a maximum length sequence "a(n)", where n=1..2N-1. Maximum length sequences are periodic sequences so "a(n)" is repeated periodically for n larger than 2N-1. Next we generate another sequence "b(n)" = "a(q*n)" where q = 2N/2+1. Kasami sequences are formed by adding "a(n)" and a time shifted version of "b(n)" modulo two. The set which is formed by taking all Kasami sequences generated by different time shifts of "b(n)" plus the "a(n)" and "b(n)" sequence forms the Kasami set of sequences. This set has 2N/2 different sequences.

References

* T. Kasami, “Weight Distribution Formula for Some Class of Cyclic Codes," Tech. Report No. R-285, Univ. of Illinois, 1966.
* L. Welch, “Lower Bounds on the Maximum Cross Correlation of Signals,” IEEE Trans. on Info. Theory, vol. 20, no. 3, pp. 397–399, May 1974.


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