Kasami code
{{distinguish|Konami Code}}
Kasami sequences are binary sequences of length {{math|2N−1}} where {{mvar|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.
Kasami Set
The process of generating a Kasami sequence is initiated by generating a maximum length sequence {{math|a(n)}}, where {{math|n {{=}} 1…2N−1}}. Maximum length sequences are periodic sequences with a period of exactly {{math|2N−1}}. Next, a secondary sequence is derived from the initial sequence via cyclic decimation sampling as {{math|b(n) {{=}} a(q ⋅ n)}}, where {{math|q {{=}} 2N/2+1}}. Modified sequences are then formed by adding {{math|a(n)}} and cyclically time shifted versions of {{math|b(n)}} using modulo-two arithmetic, which is also termed the exclusive or (xor) operation. Computing modified sequences from all {{math|2N/2}} unique time shifts of {{math|b(n)}} forms the Kasami set of code sequences.
See also
- Gold sequence (aka Gold code)
- JPL sequence (aka JPL code)
References
- {{cite tech report |author-first=Tadao |author-last=Kasami |author-link=Tadao Kasami |title=Weight Distribution Formula for Some Class of Cyclic Codes |number=R285 |institution=University of Illinois |date=1966 |url=https://core.ac.uk/download/pdf/158319552.pdf |hdl=2142/74439}}
- {{cite journal |author-first=Lloyd Richard |author-last=Welch |author-link=Lloyd Richard Welch |title=Lower Bounds on the Maximum Cross Correlation of Signals |journal=IEEE Transactions on Information Theory |volume=20 |issue=3 |pages=397–399 |date=May 1974 |doi=10.1109/TIT.1974.1055219}}
- {{cite book |author-first=Alois M. J. |author-last=Goiser |title=Handbuch der Spread-Spectrum Technik |trans-title=Handbook of the spread-spectrum technique |language=de |publisher=Springer Verlag |publication-place=Vienna, Austria |date=1998 |edition=1 |isbn=3-211-83080-4 |chapter=4.4 Kasami-Folgen |trans-chapter=Kasami sequences}}
{{telecomm-stub}}