MinT - Information on Result #1088008

Information on Result #1088008

Linear OOA(2¹⁹⁰, 50, F₂, 4, 134) (dual of [(50, 4), 10, 135]-NRT-code), using concatenation of two NRT-codes based on

linear OA(32⁸, 10, F₃₂, 8) (dual of [10, 2, 9]-code or 10-arc in PG(7,32)), using
- discarding factors / shortening the dual code based on linear OA(32⁸, 32, F₃₂, 8) (dual of [32, 24, 9]-code or 32-arc in PG(7,32)), using
  - Reedâ€“Solomon code RS(24,32) [i]
linear OOA(2¹⁵, 5, F₂, 4, 14) (dual of [(5, 4), 5, 15]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,5P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
  - an explicitly constructive algebraic function field [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(2¹⁹⁰, 50, F₂, 4, 133) (dual of [(50, 4), 10, 134]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹⁹⁰, 50, F₂, 4, 132) (dual of [(50, 4), 10, 133]-NRT-code)	[i]
3	Linear OOA(2¹⁹⁰, 50, F₂, 4, 131) (dual of [(50, 4), 10, 132]-NRT-code)	[i]
4	Linear OOA(2¹⁹⁰, 50, F₂, 4, 130) (dual of [(50, 4), 10, 131]-NRT-code)	[i]
5	Linear OOA(2¹⁹⁰, 50, F₂, 4, 129) (dual of [(50, 4), 10, 130]-NRT-code)	[i]
6	Linear OOA(2¹⁸⁸, 49, F₂, 4, 132) (dual of [(49, 4), 8, 133]-NRT-code)	[i]		Truncation for OOAs
7	Linear OOA(2¹⁸⁷, 49, F₂, 4, 131) (dual of [(49, 4), 9, 132]-NRT-code)	[i]
8	Linear OOA(2¹⁸⁶, 49, F₂, 4, 130) (dual of [(49, 4), 10, 131]-NRT-code)	[i]
9	Linear OOA(2¹⁸³, 48, F₂, 4, 127) (dual of [(48, 4), 9, 128]-NRT-code)	[i]
10	Linear OOA(2¹⁸², 48, F₂, 4, 126) (dual of [(48, 4), 10, 127]-NRT-code)	[i]
11	Linear OOA(2¹⁹⁰, 25, F₂, 8, 134) (dual of [(25, 8), 10, 135]-NRT-code)	[i]		OOA Folding