MinT - Information on Result #2774673

Information on Result #2774673

Linear OOA(3²⁰⁹, 72, F₃, 4, 106) (dual of [(72, 4), 79, 107]-NRT-code), using strength reduction based on linear OOA(3²⁰⁹, 72, F₃, 4, 107) (dual of [(72, 4), 79, 108]-NRT-code), using

constructionÂ X applied to AG(4;F,80P) âŠ‚ AG(4;F,123P) [i] based on
1. linear OOA(3¹⁵², 47, F₃, 4, 107) (dual of [(47, 4), 36, 108]-NRT-code), using algebraic-geometric NRT-code AG(4;F,80P) [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(3¹⁰⁹, 47, F₃, 4, 64) (dual of [(47, 4), 79, 65]-NRT-code), using algebraic-geometric NRT-code AG(4;F,123P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48 (see above)
3. linear OOA(3⁵⁷, 25, F₃, 4, 42) (dual of [(25, 4), 43, 43]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁵⁷, 28, F₃, 4, 42) (dual of [(28, 4), 55, 43]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,69P) [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.