MinT - Information on Result #1088115

Information on Result #1088115

Linear OOA(2²²⁸, 81, F₂, 4, 86) (dual of [(81, 4), 96, 87]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(16³⁰, 27, F₁₆, 2, 28) (dual of [(27, 2), 24, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(16³⁰, 33, F₁₆, 2, 28) (dual of [(33, 2), 36, 29]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,37P) [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
    - a function field by SÃ©mirat [i]
linear OOA(2², 3, F₂, 2, 2) (dual of [(3, 2), 4, 3]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;4,2) [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²²⁸, 81, F₂, 4, 85) (dual of [(81, 4), 96, 86]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²²⁸, 81, F₂, 4, 84) (dual of [(81, 4), 96, 85]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(2²²⁹, 81, F₂, 4, 86) (dual of [(81, 4), 95, 87]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(2²³⁰, 81, F₂, 4, 86) (dual of [(81, 4), 94, 87]-NRT-code)	[i]
5	Linear OOA(2²³¹, 81, F₂, 4, 86) (dual of [(81, 4), 93, 87]-NRT-code)	[i]
6	Linear OOA(2²²⁷, 80, F₂, 4, 85) (dual of [(80, 4), 93, 86]-NRT-code)	[i]		Truncation for OOAs
7	Linear OOA(2²²⁶, 80, F₂, 4, 84) (dual of [(80, 4), 94, 85]-NRT-code)	[i]		Truncation for OOAs
8	Linear OOA(2²²⁸, 40, F₂, 7, 86) (dual of [(40, 7), 52, 87]-NRT-code)	[i]		OOA Folding
9	Linear OOA(2²²⁸, 40, F₂, 8, 86) (dual of [(40, 8), 92, 87]-NRT-code)	[i]		OOA Folding