MinT - Information on Result #2786479

Information on Result #2786479

Linear OOA(3²¹², 61, F₃, 4, 139) (dual of [(61, 4), 32, 140]-NRT-code), using 3 step truncation based on linear OOA(3²¹⁵, 62, F₃, 4, 142) (dual of [(62, 4), 33, 143]-NRT-code), using

strength reduction [i] based on linear OOA(3²¹⁵, 62, F₃, 4, 143) (dual of [(62, 4), 33, 144]-NRT-code), using
- constructionÂ X applied to AG(4;F,0P) âŠ‚ AG(4;F,29P) [i] based on
  1. linear OOA(3¹⁴³, 36, F₃, 4, 143) (dual of [(36, 4), 1, 144]-NRT-code), using algebraic-geometric NRT-code AG(4;F,0P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
  2. linear OOA(3¹¹¹, 36, F₃, 4, 85) (dual of [(36, 4), 33, 86]-NRT-code), using algebraic-geometric NRT-code AG(4;F,29P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
  3. linear OOA(3⁷², 26, F₃, 4, 57) (dual of [(26, 4), 32, 58]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3⁷², 28, F₃, 4, 57) (dual of [(28, 4), 40, 58]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,54P) [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.