MinT - Information on Result #1088131

Information on Result #1088131

Linear OOA(2²⁵⁶, 90, F₂, 4, 98) (dual of [(90, 4), 104, 99]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(16³⁴, 30, F₁₆, 2, 32) (dual of [(30, 2), 26, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(16³⁴, 33, F₁₆, 2, 32) (dual of [(33, 2), 32, 33]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,33P) [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
    - a function field by SÃ©mirat [i]
linear OOA(2², 3, F₂, 2, 2) (dual of [(3, 2), 4, 3]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;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(2²⁵⁶, 90, F₂, 4, 97) (dual of [(90, 4), 104, 98]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²⁵⁶, 90, F₂, 4, 96) (dual of [(90, 4), 104, 97]-NRT-code)	[i]		Strength Reduction for OOAs
3	Linear OOA(2²⁵⁷, 90, F₂, 4, 98) (dual of [(90, 4), 103, 99]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(2²⁵⁸, 90, F₂, 4, 98) (dual of [(90, 4), 102, 99]-NRT-code)	[i]
5	Linear OOA(2²⁵⁹, 90, F₂, 4, 98) (dual of [(90, 4), 101, 99]-NRT-code)	[i]
6	Linear OOA(2²⁵⁵, 89, F₂, 4, 97) (dual of [(89, 4), 101, 98]-NRT-code)	[i]		Truncation for OOAs
7	Linear OOA(2²⁵⁴, 89, F₂, 4, 96) (dual of [(89, 4), 102, 97]-NRT-code)	[i]		Truncation for OOAs
8	Linear OOA(2²⁵⁶, 45, F₂, 7, 98) (dual of [(45, 7), 59, 99]-NRT-code)	[i]		OOA Folding
9	Linear OOA(2²⁵⁶, 45, F₂, 8, 98) (dual of [(45, 8), 104, 99]-NRT-code)	[i]		OOA Folding