MinT - Information on Result #2765575

Information on Result #2765575

Linear OOA(2²¹⁹, 57, F₂, 4, 144) (dual of [(57, 4), 9, 145]-NRT-code), using strength reduction based on linear OOA(2²¹⁹, 57, F₂, 4, 148) (dual of [(57, 4), 9, 149]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2³¹, 10, F₂, 4, 25) (dual of [(10, 4), 9, 26]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,14P) [i] based on function field F/F₂ with g(F) = 6 and N(F) ≥ 10, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2¹⁷⁹, 47, F₂, 4, 122) (dual of [(47, 4), 9, 123]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2³¹, 10, F₂, 4, 25) (dual of [(10, 4), 9, 26]-NRT-code) (see above)
    2. linear OOA(2¹³⁹, 37, F₂, 4, 96) (dual of [(37, 4), 9, 97]-NRT-code), using
      - juxtaposition [i] based on
        linear OOA(2²⁷, 9, F₂, 4, 22) (dual of [(9, 4), 9, 23]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,13P) [i] based on function field F/F₂ with g(F) = 5 and N(F) ≥ 9, using
        an explicitly constructive algebraic function field [i]
        linear OOA(2¹⁰³, 28, F₂, 4, 73) (dual of [(28, 4), 9, 74]-NRT-code), using
        repeating each code word 2 times [i] based on linear OOA(2⁴⁷, 14, F₂, 4, 36) (dual of [(14, 4), 9, 37]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,19P) [i] based on function field F/F₂ with g(F) = 11 and N(F) ≥ 14, 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.