MinT - Information on Result #2627138

Information on Result #2627138

Linear OOA(3²¹⁸, 75, F₃, 3, 161) (dual of [(75, 3), 7, 162]-NRT-code), using strength reduction based on linear OOA(3²¹⁸, 75, F₃, 3, 165) (dual of [(75, 3), 7, 166]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(3²⁹, 12, F₃, 3, 25) (dual of [(12, 3), 7, 26]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,10P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(3¹⁸², 63, F₃, 3, 139) (dual of [(63, 3), 7, 140]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(3¹⁴, 7, F₃, 3, 13) (dual of [(7, 3), 7, 14]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,7P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(3¹⁶¹, 56, F₃, 3, 125) (dual of [(56, 3), 7, 126]-NRT-code), using
      - repeating each code word 2 times [i] based on linear OOA(3⁷⁷, 28, F₃, 3, 62) (dual of [(28, 3), 7, 63]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,21P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, 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.