MinT - Information on Result #2770964

Information on Result #2770964

Linear OOA(3¹⁴⁵, 52, F₃, 4, 89) (dual of [(52, 4), 63, 90]-NRT-code), using strength reduction based on linear OOA(3¹⁴⁵, 52, F₃, 4, 90) (dual of [(52, 4), 63, 91]-NRT-code), using

constructionÂ X applied to AG(4;F,97P) âŠ‚ AG(4;F,107P) [i] based on
1. linear OOA(3¹³⁵, 47, F₃, 4, 90) (dual of [(47, 4), 53, 91]-NRT-code), using algebraic-geometric NRT-code AG(4;F,97P) [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(3¹²⁵, 47, F₃, 4, 80) (dual of [(47, 4), 63, 81]-NRT-code), using algebraic-geometric NRT-code AG(4;F,107P) [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.