MinT - Information on Result #2812521

Information on Result #2812521

Linear OOA(3¹⁷², 89, F₃, 4, 88) (dual of [(89, 4), 184, 89]-NRT-code), using strength reduction based on linear OOA(3¹⁷², 89, F₃, 4, 89) (dual of [(89, 4), 184, 90]-NRT-code), using

constructionÂ X applied to AG(4;F,242P) âŠ‚ AG(4;F,254P) [i] based on
1. linear OOA(3¹⁶⁰, 83, F₃, 4, 89) (dual of [(83, 4), 172, 90]-NRT-code), using algebraic-geometric NRT-code AG(4;F,242P) [i] based on function field F/F₃ with g(F) = 71 and N(F) ≥ 84, using
  - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]
2. linear OOA(3¹⁴⁸, 83, F₃, 4, 77) (dual of [(83, 4), 184, 78]-NRT-code), using algebraic-geometric NRT-code AG(4;F,254P) [i] based on function field F/F₃ with g(F) = 71 and N(F) ≥ 84 (see above)
3. linear OOA(3¹², 6, F₃, 4, 11) (dual of [(6, 4), 12, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3¹², 7, F₃, 4, 11) (dual of [(7, 4), 16, 12]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(4;F,16P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
      - an explicitly constructive algebraic function field [i]

Mode: 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.