MinT - Information on Result #2624701

Information on Result #2624701

Linear OOA(3¹⁷⁸, 61, F₃, 3, 137) (dual of [(61, 3), 5, 138]-NRT-code), using strength reduction based on linear OOA(3¹⁷⁸, 61, F₃, 3, 140) (dual of [(61, 3), 5, 141]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(3¹⁶, 7, F₃, 3, 15) (dual of [(7, 3), 5, 16]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,5P) [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(3¹⁵⁷, 54, F₃, 3, 124) (dual of [(54, 3), 5, 125]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(3¹³, 6, F₃, 3, 12) (dual of [(6, 3), 5, 13]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(3¹³, 7, F₃, 3, 12) (dual of [(7, 3), 8, 13]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,8P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7 (see above)
    2. linear OOA(3¹³⁹, 48, F₃, 3, 111) (dual of [(48, 3), 5, 112]-NRT-code), using
      - repeating each code word 4 times [i] based on linear OOA(3³¹, 12, F₃, 3, 27) (dual of [(12, 3), 5, 28]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,8P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, 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.