MinT - Information on Result #1028924

Information on Result #1028924

Linear OOA(2¹⁵⁵, 55, F₂, 3, 99) (dual of [(55, 3), 10, 100]-NRT-code), using concatenation of two NRT-codes based on

linear OA(32⁹, 11, F₃₂, 9) (dual of [11, 2, 10]-code or 11-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(2¹⁵⁵, 55, F₂, 3, 98) (dual of [(55, 3), 10, 99]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹⁵⁵, 55, F₂, 3, 97) (dual of [(55, 3), 10, 98]-NRT-code)	[i]
3	Linear OOA(2¹⁵⁵, 55, F₂, 3, 96) (dual of [(55, 3), 10, 97]-NRT-code)	[i]
4	Linear OOA(2¹⁵⁵, 55, F₂, 3, 95) (dual of [(55, 3), 10, 96]-NRT-code)	[i]
5	Linear OOA(2¹⁵⁵, 55, F₂, 3, 94) (dual of [(55, 3), 10, 95]-NRT-code)	[i]
6	Linear OOA(2¹⁵⁵, 55, F₂, 3, 93) (dual of [(55, 3), 10, 94]-NRT-code)	[i]
7	Linear OOA(2¹⁵⁵, 55, F₂, 3, 92) (dual of [(55, 3), 10, 93]-NRT-code)	[i]
8	Linear OOA(2¹⁵⁵, 55, F₂, 3, 91) (dual of [(55, 3), 10, 92]-NRT-code)	[i]
9	Linear OOA(2¹⁵⁵, 55, F₂, 3, 90) (dual of [(55, 3), 10, 91]-NRT-code)	[i]
10	Linear OOA(2¹⁵⁶, 55, F₂, 3, 99) (dual of [(55, 3), 9, 100]-NRT-code)	[i]		OOA Duplication