Kasami code[1] 

Description

Member of the family of \([2^{2r}-1, 3r, 2^{2r-1} - 2^{r-1} ]\) cyclic binary linear codes.

Parent

Cousins

  • Gold code — Gold and Kasami codes are both constructed by picking a set of cyclically unrelated sequences of binary linear codes with low crosscorrelation [2,3].
  • Griesmer code — Kasami codes satisfy the Griesmer bound for certain parameters [4].

References

[1]
Kasami, Tadao. Weight distribution formula for some class of cyclic codes. Champaign, IL, USA: University of Illinois, 1966.
[2]
D. V. Sarwate and M. B. Pursley, “Crosscorrelation properties of pseudorandom and related sequences”, Proceedings of the IEEE 68, 593 (1980) DOI
[3]
T. Helleseth, C. Li, "Pseudo-Noise Sequences." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
[4]
T. Helleseth and P. Vijay Kumar, “The weight hierarchy of the Kasami codes”, Discrete Mathematics 145, 133 (1995) DOI
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Zoo Code ID: kasami

Cite as:
“Kasami code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/kasami
BibTeX:
@incollection{eczoo_kasami, title={Kasami code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/kasami} }
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Permanent link:
https://errorcorrectionzoo.org/c/kasami

Cite as:

“Kasami code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/kasami

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/bits/cyclic/kasami.yml.