MinT - Information on Result #2770385

Information on Result #2770385

Linear OOA(3¹³⁰, 52, F₃, 4, 74) (dual of [(52, 4), 78, 75]-NRT-code), using strength reduction based on linear OOA(3¹³⁰, 52, F₃, 4, 75) (dual of [(52, 4), 78, 76]-NRT-code), using

constructionÂ X applied to AG(4;F,112P) âŠ‚ AG(4;F,122P) [i] based on
1. linear OOA(3¹²⁰, 47, F₃, 4, 75) (dual of [(47, 4), 68, 76]-NRT-code), using algebraic-geometric NRT-code AG(4;F,112P) [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(3¹¹⁰, 47, F₃, 4, 65) (dual of [(47, 4), 78, 66]-NRT-code), using algebraic-geometric NRT-code AG(4;F,122P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48 (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: 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.