MinT - Information on Result #2773045

Information on Result #2773045

Linear OOA(3¹⁸³, 62, F₃, 4, 104) (dual of [(62, 4), 65, 105]-NRT-code), using strength reduction based on linear OOA(3¹⁸³, 62, F₃, 4, 105) (dual of [(62, 4), 65, 106]-NRT-code), using

constructionÂ X applied to AG(4;F,82P) âŠ‚ AG(4;F,109P) [i] based on
1. linear OOA(3¹⁵⁰, 47, F₃, 4, 105) (dual of [(47, 4), 38, 106]-NRT-code), using algebraic-geometric NRT-code AG(4;F,82P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
  - an explicitly constructive algebraic function field [i]
2. linear OOA(3¹²³, 47, F₃, 4, 78) (dual of [(47, 4), 65, 79]-NRT-code), using algebraic-geometric NRT-code AG(4;F,109P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48 (see above)
3. linear OOA(3³³, 15, F₃, 4, 26) (dual of [(15, 4), 27, 27]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3³³, 16, F₃, 4, 26) (dual of [(16, 4), 31, 27]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,37P) [i] based on function field F/F₃ with g(F) = 7 and N(F) ≥ 16, 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.