MinT - Information on Result #1028648

Information on Result #1028648

Linear OOA(2¹³⁸, 50, F₂, 3, 87) (dual of [(50, 3), 12, 88]-NRT-code), using concatenation of two NRT-codes based on

linear OA(16⁷, 10, F₁₆, 7) (dual of [10, 3, 8]-code or 10-arc in PG(6,16)), using
- discarding factors / shortening the dual code based on linear OA(16⁷, 16, F₁₆, 7) (dual of [16, 9, 8]-code or 16-arc in PG(6,16)), using
  - Reedâ€“Solomon code RS(9,16) [i]
linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,4P) [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(2¹³⁸, 50, F₂, 3, 86) (dual of [(50, 3), 12, 87]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹³⁸, 50, F₂, 3, 85) (dual of [(50, 3), 12, 86]-NRT-code)	[i]
3	Linear OOA(2¹³⁸, 50, F₂, 3, 84) (dual of [(50, 3), 12, 85]-NRT-code)	[i]
4	Linear OOA(2¹³⁷, 49, F₂, 3, 86) (dual of [(49, 3), 10, 87]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(2¹³⁶, 49, F₂, 3, 85) (dual of [(49, 3), 11, 86]-NRT-code)	[i]
6	Linear OOA(2¹³⁵, 49, F₂, 3, 84) (dual of [(49, 3), 12, 85]-NRT-code)	[i]
7	Linear OOA(2¹³⁴, 48, F₂, 3, 83) (dual of [(48, 3), 10, 84]-NRT-code)	[i]
8	Linear OOA(2¹³³, 48, F₂, 3, 82) (dual of [(48, 3), 11, 83]-NRT-code)	[i]
9	Linear OOA(2¹³¹, 47, F₂, 3, 80) (dual of [(47, 3), 10, 81]-NRT-code)	[i]
10	Linear OOA(2¹³⁰, 47, F₂, 3, 79) (dual of [(47, 3), 11, 80]-NRT-code)	[i]
11	Linear OOA(2¹²⁹, 47, F₂, 3, 78) (dual of [(47, 3), 12, 79]-NRT-code)	[i]
12	Linear OOA(2¹³⁸, 25, F₂, 6, 87) (dual of [(25, 6), 12, 88]-NRT-code)	[i]		OOA Folding