MinT - Information on Result #2784385

Information on Result #2784385

Linear OOA(2²¹⁸, 80, F₂, 4, 78) (dual of [(80, 4), 102, 79]-NRT-code), using 2 step truncation based on linear OOA(2²²⁰, 81, F₂, 4, 80) (dual of [(81, 4), 104, 81]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(16²⁸, 27, F₁₆, 2, 26) (dual of [(27, 2), 26, 27]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(16²⁸, 33, F₁₆, 2, 26) (dual of [(33, 2), 38, 27]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,39P) [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		This result only	Method
1	Linear OOA(2²¹⁸, 40, F₂, 7, 78) (dual of [(40, 7), 62, 79]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²¹⁸, 40, F₂, 8, 78) (dual of [(40, 8), 102, 79]-NRT-code)	[i]		OOA Folding