MinT - Information on Result #1086860

Information on Result #1086860

Linear OOA(2²⁴⁴, 63, F₂, 4, 168) (dual of [(63, 4), 8, 169]-NRT-code), using juxtaposition based on

linear OOA(2²⁴, 8, F₂, 4, 20) (dual of [(8, 4), 8, 21]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,11P) [i] based on function field F/F₂ with g(F) = 4 and N(F) ≥ 8, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2²¹², 55, F₂, 4, 147) (dual of [(55, 4), 8, 148]-NRT-code), using
- strength reduction [i] based on linear OOA(2²¹², 55, F₂, 4, 148) (dual of [(55, 4), 8, 149]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2⁴⁸, 14, F₂, 4, 37) (dual of [(14, 4), 8, 38]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,18P) [i] based on function field F/F₂ with g(F) = 11 and N(F) ≥ 14, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(2¹⁵⁶, 41, F₂, 4, 110) (dual of [(41, 4), 8, 111]-NRT-code), using
      - juxtaposition [i] based on
        linear OOA(2⁴⁸, 14, F₂, 4, 37) (dual of [(14, 4), 8, 38]-NRT-code) (see above)
        linear OOA(2¹⁰⁰, 27, F₂, 4, 72) (dual of [(27, 4), 8, 73]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2³², 10, F₂, 4, 26) (dual of [(10, 4), 8, 27]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,13P) [i] based on function field F/F₂ with g(F) = 6 and N(F) ≥ 10, using
        an explicitly constructive algebraic function field [i]
        linear OOA(2⁶⁰, 17, F₂, 4, 45) (dual of [(17, 4), 8, 46]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,22P) [i] based on function field F/F₂ with g(F) = 15 and N(F) ≥ 17, 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.