MinT - Information on Result #2955397

Information on Result #2955397

Linear OOA(2²⁵³, 37, F₂, 7, 212) (dual of [(37, 7), 6, 213]-NRT-code), using strength reduction based on linear OOA(2²⁵³, 37, F₂, 7, 215) (dual of [(37, 7), 6, 216]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2³⁶, 6, F₂, 7, 34) (dual of [(6, 7), 6, 35]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(7;F,7P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2²¹¹, 31, F₂, 7, 180) (dual of [(31, 7), 6, 181]-NRT-code), using
  - strength reduction [i] based on linear OOA(2²¹¹, 31, F₂, 7, 181) (dual of [(31, 7), 6, 182]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(2⁴³, 7, F₂, 7, 40) (dual of [(7, 7), 6, 41]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(7;F,8P) [i] based on function field F/F₂ with g(F) = 3 and N(F) ≥ 7, using
        an explicitly constructive algebraic function field [i]
      2. linear OOA(2¹⁶², 24, F₂, 7, 140) (dual of [(24, 7), 6, 141]-NRT-code), using
        repeating each code word 3 times [i] based on linear OOA(2⁵⁰, 8, F₂, 7, 46) (dual of [(8, 7), 6, 47]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(7;F,9P) [i] based on function field F/F₂ with g(F) = 4 and N(F) ≥ 8, 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.