MinT - Information on Result #2772480

Information on Result #2772480

Linear OOA(3¹⁷⁴, 58, F₃, 4, 104) (dual of [(58, 4), 58, 105]-NRT-code), using strength reduction based on linear OOA(3¹⁷⁴, 58, F₃, 4, 105) (dual of [(58, 4), 58, 106]-NRT-code), using

constructionÂ X applied to AG(4;F,82P) âŠ‚ AG(4;F,103P) [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(3¹²⁹, 47, F₃, 4, 84) (dual of [(47, 4), 59, 85]-NRT-code), using algebraic-geometric NRT-code AG(4;F,103P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48 (see above)
3. linear OOA(3²⁴, 11, F₃, 4, 20) (dual of [(11, 4), 20, 21]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3²⁴, 12, F₃, 4, 20) (dual of [(12, 4), 24, 21]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,27P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, 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.