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

\([2^{2r}-1, 3r, 2^{2r-1} - 2^{r-1} ]\) 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 codeCyclic Linear \(q\)-ary Constacyclic Skew-cyclic ECC

Parents

Cyclic linear binary code

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

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

Page edit log

Victor V. Albert (2023-12-03) — most recent

Cite as:

“\([2^{2r}-1, 3r, 2^{2r-1} - 2^{r-1} ]\) 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.