MinT - Information on Result #1028922

Information on Result #1028922

Linear OOA(2¹⁷⁵, 65, F₂, 3, 99) (dual of [(65, 3), 20, 100]-NRT-code), using concatenation of two NRT-codes based on

linear OA(32⁹, 13, F₃₂, 9) (dual of [13, 4, 10]-code or 13-arc in PG(8,32)), using
- discarding factors / shortening the dual code based on linear OA(32⁹, 32, F₃₂, 9) (dual of [32, 23, 10]-code or 32-arc in PG(8,32)), using
  - Reedâ€“Solomon code RS(23,32) [i]
linear OOA(2¹⁰, 5, F₂, 3, 9) (dual of [(5, 3), 5, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;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(2¹⁷⁵, 65, F₂, 3, 98) (dual of [(65, 3), 20, 99]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹⁷⁵, 65, F₂, 3, 97) (dual of [(65, 3), 20, 98]-NRT-code)	[i]
3	Linear OOA(2¹⁷⁵, 65, F₂, 3, 96) (dual of [(65, 3), 20, 97]-NRT-code)	[i]
4	Linear OOA(2¹⁷⁴, 64, F₂, 3, 98) (dual of [(64, 3), 18, 99]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(2¹⁷³, 64, F₂, 3, 97) (dual of [(64, 3), 19, 98]-NRT-code)	[i]
6	Linear OOA(2¹⁷², 64, F₂, 3, 96) (dual of [(64, 3), 20, 97]-NRT-code)	[i]
7	Linear OOA(2¹⁷¹, 63, F₂, 3, 95) (dual of [(63, 3), 18, 96]-NRT-code)	[i]
8	Linear OOA(2¹⁷⁰, 63, F₂, 3, 94) (dual of [(63, 3), 19, 95]-NRT-code)	[i]
9	Linear OOA(2¹⁶⁸, 62, F₂, 3, 92) (dual of [(62, 3), 18, 93]-NRT-code)	[i]
10	Linear OOA(2¹⁷⁵, 32, F₂, 6, 99) (dual of [(32, 6), 17, 100]-NRT-code)	[i]		OOA Folding