MinT - Information on Result #2765916

Information on Result #2765916

Linear OOA(2²²⁴, 78, F₂, 4, 85) (dual of [(78, 4), 88, 86]-NRT-code), using strength reduction based on linear OOA(2²²⁴, 78, F₂, 4, 86) (dual of [(78, 4), 88, 87]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(16³⁰, 26, F₁₆, 2, 28) (dual of [(26, 2), 22, 29]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(16³⁰, 33, F₁₆, 2, 28) (dual of [(33, 2), 36, 29]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,37P) [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
      - a function field by SÃ©mirat [i]
2. 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		Method
1	Linear OOA(2²²⁵, 78, F₂, 4, 85) (dual of [(78, 4), 87, 86]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²²⁶, 78, F₂, 4, 85) (dual of [(78, 4), 86, 86]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²²³, 77, F₂, 4, 84) (dual of [(77, 4), 85, 85]-NRT-code)	[i]	Truncation for OOAs
4	Linear OOA(2²²⁴, 39, F₂, 7, 85) (dual of [(39, 7), 49, 86]-NRT-code)	[i]	OOA Folding
5	Linear OOA(2²²⁴, 39, F₂, 8, 85) (dual of [(39, 8), 88, 86]-NRT-code)	[i]	OOA Folding