MinT - Information on Result #2776436

Information on Result #2776436

Linear OOA(3²³⁴, 61, F₃, 4, 181) (dual of [(61, 4), 10, 182]-NRT-code), using strength reduction based on linear OOA(3²³⁴, 61, F₃, 4, 184) (dual of [(61, 4), 10, 185]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(3³⁰, 10, F₃, 4, 27) (dual of [(10, 4), 10, 28]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,12P) [i] based on function field F/F₃ with g(F) = 3 and N(F) ≥ 10, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(3¹⁹⁴, 51, F₃, 4, 156) (dual of [(51, 4), 10, 157]-NRT-code), using
  - strength reduction [i] based on linear OOA(3¹⁹⁴, 51, F₃, 4, 157) (dual of [(51, 4), 10, 158]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(3⁸², 23, F₃, 4, 69) (dual of [(23, 4), 10, 70]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(3⁸², 24, F₃, 4, 69) (dual of [(24, 4), 14, 70]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,26P) [i] based on function field F/F₃ with g(F) = 13 and N(F) ≥ 24, using
        a function field by SÃ©mirat [i]
      2. linear OOA(3¹⁰², 28, F₃, 4, 87) (dual of [(28, 4), 10, 88]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,24P) [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.