MinT - Information on Result #1009758

Information on Result #1009758

Linear OOA(2¹⁰⁵, 40, F₂, 3, 55) (dual of [(40, 3), 15, 56]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁴⁶, 20, F₂, 3, 27) (dual of [(20, 3), 14, 28]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,32P) [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2⁵⁹, 20, F₂, 3, 55) (dual of [(20, 3), 1, 56]-NRT-code), using
- strength reduction [i] based on linear OOA(2⁵⁹, 20, F₂, 3, 59) (dual of [(20, 3), 1, 60]-NRT-code), using
  - dual of repetition NRT-code with length 20 [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(2¹⁷³, 80, F₂, 3, 55) (dual of [(80, 3), 67, 56]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²²⁴, 80, F₂, 3, 110) (dual of [(80, 3), 16, 111]-NRT-code)	[i]
3	Linear OOA(2²²⁴, 80, F₂, 3, 111) (dual of [(80, 3), 16, 112]-NRT-code)	[i]
4	Linear OOA(2¹⁵⁰, 55, F₂, 3, 73) (dual of [(55, 3), 15, 74]-NRT-code)	[i]		Juxtaposition for OOAs
5	Linear OOA(2¹⁵⁶, 57, F₂, 3, 77) (dual of [(57, 3), 15, 78]-NRT-code)	[i]
6	Linear OOA(2¹⁶⁵, 60, F₂, 3, 82) (dual of [(60, 3), 15, 83]-NRT-code)	[i]
7	Linear OOA(2¹⁶⁸, 61, F₂, 3, 83) (dual of [(61, 3), 15, 84]-NRT-code)	[i]
8	Linear OOA(2²⁰¹, 72, F₂, 3, 98) (dual of [(72, 3), 15, 99]-NRT-code)	[i]
9	Linear OOA(2²⁰⁴, 73, F₂, 3, 101) (dual of [(73, 3), 15, 102]-NRT-code)	[i]