MinT - Information on Result #2221949

Information on Result #2221949

Linear OA(2¹⁰⁸, 164, F₂, 34) (dual of [164, 56, 35]-code), using 1 times truncation based on linear OA(2¹⁰⁹, 165, F₂, 35) (dual of [165, 56, 36]-code), using

concatenation of two codes [i] based on
1. linear OA(16¹⁹, 33, F₁₆, 17) (dual of [33, 14, 18]-code), using
  - extended algebraic-geometric code AG_e(F,15P) [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
    - a function field by SÃ©mirat [i]
2. linear OA(2¹, 5, F₂, 1) (dual of [5, 4, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OA(2¹¹⁰, 166, F₂, 34) (dual of [166, 56, 35]-code)	[i]	Code Embedding in Larger Space
2	Linear OA(2¹¹¹, 167, F₂, 34) (dual of [167, 56, 35]-code)	[i]
3	Linear OA(2¹¹², 168, F₂, 34) (dual of [168, 56, 35]-code)	[i]
4	Linear OA(2¹¹², 169, F₂, 34) (dual of [169, 57, 35]-code)	[i]	ConstructionÂ X with VarÅ¡amov Bound
5	Linear OOA(2¹⁰⁸, 82, F₂, 2, 34) (dual of [(82, 2), 56, 35]-NRT-code)	[i]	OOA Folding
6	Linear OOA(2¹⁰⁸, 54, F₂, 3, 34) (dual of [(54, 3), 54, 35]-NRT-code)	[i]	OOA Folding