MinT - Information on Result #1028904

Information on Result #1028904

Linear OOA(2²⁵⁸, 111, F₂, 3, 109) (dual of [(111, 3), 75, 110]-NRT-code), using concatenation of two NRT-codes based on

linear OA(32²², 37, F₃₂, 21) (dual of [37, 15, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(32²², 43, F₃₂, 21) (dual of [43, 21, 22]-code), using
  - algebraic-geometric code AG(F,21P) [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
    - a function field by SÃ©mirat [i]
linear OOA(2⁴, 3, F₂, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(3;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(2²⁵⁸, 111, F₂, 3, 108) (dual of [(111, 3), 75, 109]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²⁵⁹, 111, F₂, 3, 109) (dual of [(111, 3), 74, 110]-NRT-code)	[i]		OOA Duplication
3	Linear OOA(2²⁶⁰, 111, F₂, 3, 109) (dual of [(111, 3), 73, 110]-NRT-code)	[i]		OOA Duplication
4	Linear OOA(2²⁵⁷, 110, F₂, 3, 108) (dual of [(110, 3), 73, 109]-NRT-code)	[i]		Truncation for OOAs
5	Linear OOA(2²⁵⁶, 110, F₂, 3, 107) (dual of [(110, 3), 74, 108]-NRT-code)	[i]
6	Linear OOA(2²⁵⁵, 110, F₂, 3, 106) (dual of [(110, 3), 75, 107]-NRT-code)	[i]
7	Linear OOA(2²⁵⁴, 109, F₂, 3, 105) (dual of [(109, 3), 73, 106]-NRT-code)	[i]
8	Linear OOA(2²⁵⁸, 55, F₂, 6, 109) (dual of [(55, 6), 72, 110]-NRT-code)	[i]		OOA Folding