MinT - Information on Result #2811534

Information on Result #2811534

Linear OOA(3¹³⁰, 68, F₃, 4, 70) (dual of [(68, 4), 142, 71]-NRT-code), using strength reduction based on linear OOA(3¹³⁰, 68, F₃, 4, 71) (dual of [(68, 4), 142, 72]-NRT-code), using

constructionÂ X applied to AG(4;F,180P) âŠ‚ AG(4;F,190P) [i] based on
1. linear OOA(3¹²⁰, 63, F₃, 4, 71) (dual of [(63, 4), 132, 72]-NRT-code), using algebraic-geometric NRT-code AG(4;F,180P) [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64, using
  - a curve from the manYPoints database [i]
2. linear OOA(3¹¹⁰, 63, F₃, 4, 61) (dual of [(63, 4), 142, 62]-NRT-code), using algebraic-geometric NRT-code AG(4;F,190P) [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64 (see above)
3. linear OOA(3¹⁰, 5, F₃, 4, 9) (dual of [(5, 4), 10, 10]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3¹⁰, 7, F₃, 4, 9) (dual of [(7, 4), 18, 10]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,18P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
      - an explicitly constructive algebraic function field [i]

Mode: 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.