MinT - Information on Result #2659355

Information on Result #2659355

Linear OOA(3¹¹⁵, 44, F₃, 3, 76) (dual of [(44, 3), 17, 77]-NRT-code), using 3 step truncation based on linear OOA(3¹¹⁸, 45, F₃, 3, 79) (dual of [(45, 3), 17, 80]-NRT-code), using

constructionÂ X applied to AG(3;F,0P) âŠ‚ AG(3;F,31P) [i] based on
1. linear OOA(3⁸⁰, 27, F₃, 3, 80) (dual of [(27, 3), 1, 81]-NRT-code), using algebraic-geometric NRT-code AG(3;F,0P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
  - an explicitly constructive algebraic function field [i]
2. linear OOA(3⁶⁴, 27, F₃, 3, 49) (dual of [(27, 3), 17, 50]-NRT-code), using algebraic-geometric NRT-code AG(3;F,31P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
3. linear OOA(3³⁸, 18, F₃, 3, 29) (dual of [(18, 3), 16, 30]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3³⁸, 19, F₃, 3, 29) (dual of [(19, 3), 19, 30]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,27P) [i] based on function field F/F₃ with g(F) = 9 and N(F) ≥ 19, 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.