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\([2^{2r}-1, 3r, 2^{2r-1} - 2^{r-1} ]\) Kasami code[1]

Description

Member of the family of \([2^{2r}-1, 3r, 2^{2r-1} - 2^{r-1} ]\) cyclic binary linear codes. Gold and Kasami codes are both constructed by picking a set of cyclically unrelated sequences of binary linear codes with low cross-correlation [2,3].

Cousins

  • \([2^r-1, 2r ]\) Gold code— Gold and Kasami codes are both constructed by picking a set of cyclically unrelated sequences of binary linear codes with low cross-correlation [2,3].
  • Griesmer code— Kasami codes satisfy the Griesmer bound for certain parameters [4].

Member of code lists

Primary Hierarchy

Classical Domain
Binary Kingdom
Binary codeECC
Binary group-orbit codeECC
Linear binary codeLinear \(q\)-ary Linear code over \(\mathbb{Z}_q\) ECC
Cyclic linear binary codeLinear \(q\)-ary Cyclic Constacyclic Skew-cyclic ECC
Parents
Cyclic linear binary code
\([2^{2r}-1, 3r, 2^{2r-1} - 2^{r-1} ]\) Kasami code

References

[1]
T. Kasami. 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), pp. 613-644 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:
“\([2^{2r}-1, 3r, 2^{2r-1} - 2^{r-1} ]\) Kasami code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/kasami, arXiv:2606.11484
BibTeX:
@incollection{eczoo_kasami,
title={\([2^{2r}-1, 3r, 2^{2r-1} - 2^{r-1} ]\) Kasami code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/kasami}
}
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Permanent link:
https://errorcorrectionzoo.org/c/kasami

Cite as:

“\([2^{2r}-1, 3r, 2^{2r-1} - 2^{r-1} ]\) Kasami code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/kasami, arXiv:2606.11484

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