MinT - Information on Result #2812967

Information on Result #2812967

Linear OOA(3¹⁸⁹, 69, F₃, 4, 127) (dual of [(69, 4), 87, 128]-NRT-code), using strength reduction based on linear OOA(3¹⁸⁹, 69, F₃, 4, 128) (dual of [(69, 4), 87, 129]-NRT-code), using

constructionÂ X applied to AG(4;F,123P) âŠ‚ AG(4;F,135P) [i] based on
1. linear OOA(3¹⁷⁷, 63, F₃, 4, 128) (dual of [(63, 4), 75, 129]-NRT-code), using algebraic-geometric NRT-code AG(4;F,123P) [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64, using
  - a curve from the manYPoints database [i]
2. linear OOA(3¹⁶⁵, 63, F₃, 4, 116) (dual of [(63, 4), 87, 117]-NRT-code), using algebraic-geometric NRT-code AG(4;F,135P) [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64 (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.