MinT - Information on Result #908999

Information on Result #908999

Linear OOA(2¹¹³, 58, F₂, 2, 80) (dual of [(58, 2), 3, 81]-NRT-code), using juxtaposition based on

linear OOA(2³, 3, F₂, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;3,2) [i]
linear OOA(2¹⁰⁷, 55, F₂, 2, 76) (dual of [(55, 2), 3, 77]-NRT-code), using
- repeating each code word 11 times [i] based on linear OOA(2⁷, 5, F₂, 2, 6) (dual of [(5, 2), 3, 7]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,3P) [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(2¹¹³, 58, F₂, 2, 79) (dual of [(58, 2), 3, 80]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹¹³, 58, F₂, 2, 78) (dual of [(58, 2), 3, 79]-NRT-code)	[i]
3	Linear OOA(2¹¹³, 58, F₂, 2, 77) (dual of [(58, 2), 3, 78]-NRT-code)	[i]
4	Linear OOA(2¹¹³, 58, F₂, 2, 76) (dual of [(58, 2), 3, 77]-NRT-code)	[i]
5	Linear OOA(2¹¹³, 58, F₂, 2, 75) (dual of [(58, 2), 3, 76]-NRT-code)	[i]
6	Linear OOA(2¹¹³, 58, F₂, 2, 74) (dual of [(58, 2), 3, 75]-NRT-code)	[i]
7	Linear OOA(2¹⁰⁸, 55, F₂, 2, 75) (dual of [(55, 2), 2, 76]-NRT-code)	[i]		Truncation for OOAs
8	Linear OOA(2¹⁰⁵, 54, F₂, 2, 72) (dual of [(54, 2), 3, 73]-NRT-code)	[i]
9	Linear OOA(2¹⁰⁴, 53, F₂, 2, 71) (dual of [(53, 2), 2, 72]-NRT-code)	[i]
10	Linear OOA(2¹¹⁹, 61, F₂, 2, 84) (dual of [(61, 2), 3, 85]-NRT-code)	[i]		Juxtaposition for OOAs
11	Linear OOA(2¹¹³, 29, F₂, 4, 80) (dual of [(29, 4), 3, 81]-NRT-code)	[i]		OOA Folding