MinT - Information on Result #2623118

Information on Result #2623118

Linear OOA(3¹⁴⁷, 51, F₃, 3, 112) (dual of [(51, 3), 6, 113]-NRT-code), using strength reduction based on linear OOA(3¹⁴⁷, 51, F₃, 3, 114) (dual of [(51, 3), 6, 115]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(3³⁰, 12, F₃, 3, 26) (dual of [(12, 3), 6, 27]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,9P) [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(3¹¹¹, 39, F₃, 3, 87) (dual of [(39, 3), 6, 88]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(3²⁷, 11, F₃, 3, 23) (dual of [(11, 3), 6, 24]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(3²⁷, 12, F₃, 3, 23) (dual of [(12, 3), 9, 24]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,12P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12 (see above)
    2. linear OOA(3⁷⁸, 28, F₃, 3, 63) (dual of [(28, 3), 6, 64]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,20P) [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.