MinT - Information on Result #1028552

Information on Result #1028552

Linear OOA(2¹⁷⁸, 66, F₂, 3, 101) (dual of [(66, 3), 20, 102]-NRT-code), using concatenation of two NRT-codes based on

linear OA(16¹⁷, 22, F₁₆, 16) (dual of [22, 5, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(16¹⁷, 24, F₁₆, 16) (dual of [24, 7, 17]-code), using
  - extended algebraic-geometric code AG_e(F,7P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]
linear OOA(2⁵, 3, F₂, 3, 5) (dual of [(3, 3), 4, 6]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(3;4,2) [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(2¹⁷⁸, 66, F₂, 3, 100) (dual of [(66, 3), 20, 101]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹⁷⁸, 66, F₂, 3, 99) (dual of [(66, 3), 20, 100]-NRT-code)	[i]
3	Linear OOA(2¹⁷⁸, 66, F₂, 3, 98) (dual of [(66, 3), 20, 99]-NRT-code)	[i]
4	Linear OOA(2¹⁷⁸, 66, F₂, 3, 97) (dual of [(66, 3), 20, 98]-NRT-code)	[i]
5	Linear OOA(2¹⁷⁹, 66, F₂, 3, 101) (dual of [(66, 3), 19, 102]-NRT-code)	[i]		OOA Duplication
6	Linear OOA(2¹⁸⁰, 66, F₂, 3, 101) (dual of [(66, 3), 18, 102]-NRT-code)	[i]		OOA Duplication
7	Linear OOA(2¹⁷⁷, 65, F₂, 3, 100) (dual of [(65, 3), 18, 101]-NRT-code)	[i]		Truncation for OOAs
8	Linear OOA(2¹⁷⁶, 65, F₂, 3, 99) (dual of [(65, 3), 19, 100]-NRT-code)	[i]
9	Linear OOA(2¹⁷⁴, 64, F₂, 3, 97) (dual of [(64, 3), 18, 98]-NRT-code)	[i]
10	Linear OOA(2¹⁷³, 64, F₂, 3, 96) (dual of [(64, 3), 19, 97]-NRT-code)	[i]
11	Linear OOA(2¹⁷², 64, F₂, 3, 95) (dual of [(64, 3), 20, 96]-NRT-code)	[i]
12	Linear OOA(2¹⁷¹, 63, F₂, 3, 94) (dual of [(63, 3), 18, 95]-NRT-code)	[i]
13	Linear OOA(2¹⁷⁰, 63, F₂, 3, 93) (dual of [(63, 3), 19, 94]-NRT-code)	[i]
14	Linear OOA(2¹⁷⁸, 33, F₂, 6, 101) (dual of [(33, 6), 20, 102]-NRT-code)	[i]		OOA Folding