\(ED_m\) code[1]

Description

Also called an equidistant code with maximal distance. Member of the family of \( (c\frac{qt-1}{(t-1,q-1)},qt,ct\frac{q-1}{(t-1,q-1)}) \) \(q\)-ary codes, where \(c,t\geq 1\) and \((a,b)\) is the greatest common divisor of \(a\) and \(b\). Such codes are universally optimal and are related to resolvable block designs.

Parent

References

[1]
N. V. Semakov, V. A. Zinoviev, “Equidistant q-ary Codes with Maximal Distance and Resolvable Balanced Incomplete Block Designs”, Probl. Peredachi Inf., 4:2 (1968), 3–10; Problems Inform. Transmission, 4:2 (1968), 1–7
[2]
W. C. Huffman, J.-L. Kim, and P. Solé, Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
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Zoo Code ID: semakov_zinoviev

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

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

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/classical/q-ary_digits/universally_optimal/semakov_zinoviev.yml.