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codes/classical/matrices/subspace/subspace.yml

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@@ -7,7 +7,7 @@ code_id: subspace
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physical: matrices
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name: 'Subspace code'
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introduced: '\cite{arXiv:cs/0703061,arxiv:0805.3824}'
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introduced: '\cite{arXiv:cs/0703061,arxiv:0805.3824,arxiv:1103.3117}'
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description: |
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- code_id: matrices_into_matrices
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detail: 'Subspace codes are represented my generator matrices of subspaces of \(\mathbb{F}_q^n\).'
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detail: 'Subspace codes are represented by generator matrices of subspaces of \(\mathbb{F}_q^n\).'
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cousins:
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- code_id: projective
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detail: 'Subspace codes are sets of subspaces of a projective space \(PG(n-1,q)\).'

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

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- 'Equidistant code with maximal distance'
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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 \(b\).
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Member of a family of nonlinear \( (c\frac{qt-1}{(t-1,q-1)},qt,ct\frac{q-1}{(t-1,q-1)}) \) \(q\)-ary codes, where \(c,t\geq 1\) and \((a,b)\) is the greatest common divisor of \(a\) and \(b\).
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Such codes are universally optimal and are related to resolvable block designs.
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codes/classical/q-ary_digits/universally_optimal/semakov_zinoviev_zaitsev.yml

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introduced: '\cite{manual:{N. V. Semakov, V. A. Zinoviev, G. V. Zaitsev, “A Class of Maximum Equidistant Codes”, Probl. Peredachi Inf., 5:2 (1969), 84–87; Problems Inform. Transmission, 5:2 (1969), 65–68}}'
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Member of a family that is related to affine resolvable block designs and that is universally optimal.
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Member of a nonlinear \(q\)-ary code family that is related to affine resolvable block designs and that is universally optimal.
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