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\(ED_m\) code[1]

Alternative names: Equidistant code with maximal distance.

Description

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.

Member of code lists

Primary Hierarchy

Classical Domain
Galois-field Kingdom
\(q\)-ary codeECC
Universally optimal \(q\)-ary codeUniversally optimal ECC
\(q\)-ary sharp configurationOA Sharp configuration \(t\)-design Universally optimal ECC
Parents
\(q\)-ary sharp configuration
The \(ED_m\) code is a \(q\)-ary sharp configuration [2; Table 12.1].
\(ED_m\) code

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]
P. Boyvalenkov, D. Danev, "Linear programming bounds." 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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Permanent link:
https://errorcorrectionzoo.org/c/semakov_zinoviev

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/edit/main/codes/classical/q-ary_digits/universally_optimal/semakov_zinoviev.yml.