MinT - Information on Result #908655

Information on Result #908655

Linear OOA(2¹⁴¹, 74, F₂, 2, 74) (dual of [(74, 2), 7, 75]-NRT-code), using juxtaposition based on

linear OOA(2⁶³, 35, F₂, 2, 35) (dual of [(35, 2), 7, 36]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²⁸, 17, F₂, 2, 17) (dual of [(17, 2), 6, 18]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2¹¹, 8, F₂, 2, 8) (dual of [(8, 2), 5, 9]-NRT-code), using
        an explicit generator matrix by Edel [i]
      2. linear OOA(2¹⁷, 9, F₂, 2, 17) (dual of [(9, 2), 1, 18]-NRT-code), using
        dual of repetition NRT-code with length 9 [i]
  2. linear OOA(2³⁵, 18, F₂, 2, 35) (dual of [(18, 2), 1, 36]-NRT-code), using
    - dual of repetition NRT-code with length 18 [i]
linear OOA(2⁷¹, 39, F₂, 2, 38) (dual of [(39, 2), 7, 39]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁷¹, 41, F₂, 2, 38) (dual of [(41, 2), 11, 39]-NRT-code), using
  - 1 step truncation [i] based on linear OOA(2⁷², 42, F₂, 2, 39) (dual of [(42, 2), 12, 40]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(8¹⁰, 14, F₈, 9) (dual of [14, 4, 10]-code), using
        extended algebraic-geometric code AG_e(F,4P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
        F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
      2. linear OOA(2³, 3, F₂, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;3,2) [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

None.