MinT - Information on Result #2765081

Information on Result #2765081

Linear OOA(2²¹¹, 57, F₂, 4, 125) (dual of [(57, 4), 17, 126]-NRT-code), using strength reduction based on linear OOA(2²¹¹, 57, F₂, 4, 126) (dual of [(57, 4), 17, 127]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2⁵¹, 17, F₂, 4, 36) (dual of [(17, 4), 17, 37]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,31P) [i] based on function field F/F₂ with g(F) = 15 and N(F) ≥ 17, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2¹⁴³, 40, F₂, 4, 89) (dual of [(40, 4), 17, 90]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(2¹⁴³, 41, F₂, 4, 89) (dual of [(41, 4), 21, 90]-NRT-code), using
    - algebraic-geometric NRT-code AG(4;F,74P) [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
      - an explicitly constructive algebraic function field [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

None.