MinT - Information on Result #2712540

Information on Result #2712540

Linear OOA(3¹⁷⁸, 89, F₃, 3, 97) (dual of [(89, 3), 89, 98]-NRT-code), using strength reduction based on linear OOA(3¹⁷⁸, 89, F₃, 3, 98) (dual of [(89, 3), 89, 99]-NRT-code), using

constructionÂ X applied to AG(3;F,150P) âŠ‚ AG(3;F,159P) [i] based on
1. linear OOA(3¹⁶⁹, 83, F₃, 3, 98) (dual of [(83, 3), 80, 99]-NRT-code), using algebraic-geometric NRT-code AG(3;F,150P) [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(3¹⁶⁰, 83, F₃, 3, 89) (dual of [(83, 3), 89, 90]-NRT-code), using algebraic-geometric NRT-code AG(3;F,159P) [i] based on function field F/F₃ with g(F) = 71 and N(F) ≥ 84 (see above)
3. linear OOA(3⁹, 6, F₃, 3, 8) (dual of [(6, 3), 9, 9]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(3⁹, 7, F₃, 3, 8) (dual of [(7, 3), 12, 9]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,12P) [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.