MinT - Information on Result #1086971

Information on Result #1086971

Linear OOA(2²¹⁴, 55, F₂, 4, 157) (dual of [(55, 4), 6, 158]-NRT-code), using juxtaposition based on

linear OOA(2¹⁸, 6, F₂, 4, 16) (dual of [(6, 4), 6, 17]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;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]
linear OOA(2¹⁹⁰, 49, F₂, 4, 140) (dual of [(49, 4), 6, 141]-NRT-code), using
- strength reduction [i] based on linear OOA(2¹⁹⁰, 49, F₂, 4, 141) (dual of [(49, 4), 6, 142]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2³⁰, 9, F₂, 4, 25) (dual of [(9, 4), 6, 26]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,10P) [i] based on function field F/F₂ with g(F) = 5 and N(F) ≥ 9, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(2¹⁵⁴, 40, F₂, 4, 115) (dual of [(40, 4), 6, 116]-NRT-code), using
      - repeating each code word 4 times [i] based on linear OOA(2³⁴, 10, F₂, 4, 28) (dual of [(10, 4), 6, 29]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,11P) [i] based on function field F/F₂ with g(F) = 6 and N(F) ≥ 10, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

None.

The following results depend on this result: