MinT - Information on Result #2813854

Information on Result #2813854

Linear OOA(3²¹⁹, 100, F₃, 4, 119) (dual of [(100, 4), 181, 120]-NRT-code), using strength reduction based on linear OOA(3²¹⁹, 100, F₃, 4, 120) (dual of [(100, 4), 181, 121]-NRT-code), using

constructionÂ X applied to AG(4;F,259P) âŠ‚ AG(4;F,269P) [i] based on
1. linear OOA(3²⁰⁹, 95, F₃, 4, 120) (dual of [(95, 4), 171, 121]-NRT-code), using algebraic-geometric NRT-code AG(4;F,259P) [i] based on function field F/F₃ with g(F) = 89 and N(F) ≥ 96, using
  - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]
2. linear OOA(3¹⁹⁹, 95, F₃, 4, 110) (dual of [(95, 4), 181, 111]-NRT-code), using algebraic-geometric NRT-code AG(4;F,269P) [i] based on function field F/F₃ with g(F) = 89 and N(F) ≥ 96 (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: 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.