MinT - Information on Result #1087972

Information on Result #1087972

Linear OOA(2¹⁹⁸, 57, F₂, 4, 111) (dual of [(57, 4), 30, 112]-NRT-code), using concatenation of two NRT-codes based on

linear OA(32¹³, 19, F₃₂, 13) (dual of [19, 6, 14]-code or 19-arc in PG(12,32)), using
- discarding factors / shortening the dual code based on linear OA(32¹³, 32, F₃₂, 13) (dual of [32, 19, 14]-code or 32-arc in PG(12,32)), using
  - Reedâ€“Solomon code RS(19,32) [i]
linear OOA(2⁷, 3, F₂, 4, 7) (dual of [(3, 4), 5, 8]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(4;5,2) [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(2¹⁹⁸, 57, F₂, 4, 110) (dual of [(57, 4), 30, 111]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹⁹⁸, 57, F₂, 4, 109) (dual of [(57, 4), 30, 110]-NRT-code)	[i]
3	Linear OOA(2¹⁹⁸, 57, F₂, 4, 108) (dual of [(57, 4), 30, 109]-NRT-code)	[i]
4	Linear OOA(2¹⁹⁸, 57, F₂, 4, 107) (dual of [(57, 4), 30, 108]-NRT-code)	[i]
5	Linear OOA(2¹⁹⁹, 57, F₂, 4, 111) (dual of [(57, 4), 29, 112]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(2²⁰⁰, 57, F₂, 4, 111) (dual of [(57, 4), 28, 112]-NRT-code)	[i]
7	Linear OOA(2²⁰¹, 57, F₂, 4, 111) (dual of [(57, 4), 27, 112]-NRT-code)	[i]
8	Linear OOA(2¹⁹⁷, 56, F₂, 4, 110) (dual of [(56, 4), 27, 111]-NRT-code)	[i]		Truncation for OOAs
9	Linear OOA(2¹⁹⁶, 56, F₂, 4, 109) (dual of [(56, 4), 28, 110]-NRT-code)	[i]
10	Linear OOA(2¹⁹⁵, 56, F₂, 4, 108) (dual of [(56, 4), 29, 109]-NRT-code)	[i]
11	Linear OOA(2¹⁹⁴, 56, F₂, 4, 107) (dual of [(56, 4), 30, 108]-NRT-code)	[i]
12	Linear OOA(2¹⁹⁸, 28, F₂, 8, 111) (dual of [(28, 8), 26, 112]-NRT-code)	[i]		OOA Folding