MinT - Information on Result #2848812

Information on Result #2848812

Linear OOA(2²⁵⁸, 53, F₂, 5, 196) (dual of [(53, 5), 7, 197]-NRT-code), using strength reduction based on linear OOA(2²⁵⁸, 53, F₂, 5, 198) (dual of [(53, 5), 7, 199]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2²⁸, 7, F₂, 5, 25) (dual of [(7, 5), 7, 26]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(5;F,9P) [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(2²²³, 46, F₂, 5, 172) (dual of [(46, 5), 7, 173]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2²⁸, 7, F₂, 5, 25) (dual of [(7, 5), 7, 26]-NRT-code) (see above)
    2. linear OOA(2¹⁸⁸, 39, F₂, 5, 146) (dual of [(39, 5), 7, 147]-NRT-code), using
      - strength reduction [i] based on linear OOA(2¹⁸⁸, 39, F₂, 5, 147) (dual of [(39, 5), 7, 148]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2³⁸, 9, F₂, 5, 33) (dual of [(9, 5), 7, 34]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(5;F,11P) [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(2¹⁴³, 30, F₂, 5, 113) (dual of [(30, 5), 7, 114]-NRT-code), using
        repeating each code word 3 times [i] based on linear OOA(2⁴³, 10, F₂, 5, 37) (dual of [(10, 5), 7, 38]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(5;F,12P) [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.

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.