MinT - Information on Result #2844821

Information on Result #2844821

Linear OOA(2²¹¹, 43, F₂, 5, 171) (dual of [(43, 5), 4, 172]-NRT-code), using strength reduction based on linear OOA(2²¹¹, 43, F₂, 5, 179) (dual of [(43, 5), 4, 180]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2²¹, 5, F₂, 5, 20) (dual of [(5, 5), 4, 21]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(5;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2¹⁸⁶, 38, F₂, 5, 158) (dual of [(38, 5), 4, 159]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2²¹, 5, F₂, 5, 20) (dual of [(5, 5), 4, 21]-NRT-code) (see above)
    2. linear OOA(2¹⁶¹, 33, F₂, 5, 137) (dual of [(33, 5), 4, 138]-NRT-code), using
      - juxtaposition [i] based on
        linear OOA(2²¹, 5, F₂, 5, 20) (dual of [(5, 5), 4, 21]-NRT-code) (see above)
        linear OOA(2¹³⁶, 28, F₂, 5, 116) (dual of [(28, 5), 4, 117]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2²¹, 5, F₂, 5, 20) (dual of [(5, 5), 4, 21]-NRT-code) (see above)
        linear OOA(2¹¹¹, 23, F₂, 5, 95) (dual of [(23, 5), 4, 96]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(2²¹, 5, F₂, 5, 20) (dual of [(5, 5), 4, 21]-NRT-code) (see above)
        linear OOA(2⁸⁶, 18, F₂, 5, 74) (dual of [(18, 5), 4, 75]-NRT-code), using
        repeating each code word 3 times [i] based on linear OOA(2²⁶, 6, F₂, 5, 24) (dual of [(6, 5), 4, 25]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(5;F,5P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, 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.