\([[2^r-1, 2^r-2r-1, 3]]_p\) prime-qudit CSS code

\([[2^r-1, 2^r-2r-1, 3]]_p\) prime-qudit CSS code[1]

Description

A family of CSS codes extending Hamming-based CSS codes to prime qudits of dimension \(p\) by expressing the qubit code stabilizers in local-dimension-invariant (LDI) form [1].

Parent

Modular-qudit CSS code

Cousin

\([[2^r-1, 2^r-2r-1, 3]]\) Hamming-based CSS code — \([[2^r-1, 2^r-2r-1, 3]]_p\) codes are prime-qudit extensions of \([[2^r-1, 2^r-2r-1, 3]]\) codes.

References

[1]: Arun J. Moorthy and Lane G. Gunderman, “Local-dimension-invariant Calderbank-Shor-Steane Codes with an Improved Distance Promise”. 2110.11510

Cite as:

“\([[2^r-1, 2^r-2r-1, 3]]_p\) prime-qudit CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/qudit_hamming_css

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qudits/qudit_hamming_css.yml.