MinT - Information on Result #2636048

Information on Result #2636048

Linear OOA(4²²³, 149, F₄, 3, 84) (dual of [(149, 3), 224, 85]-NRT-code), using strength reduction based on linear OOA(4²²³, 149, F₄, 3, 85) (dual of [(149, 3), 224, 86]-NRT-code), using

constructionÂ X applied to AG(3;F,301P) âŠ‚ AG(3;F,328P) [i] based on
1. linear OOA(4¹⁹⁰, 129, F₄, 3, 85) (dual of [(129, 3), 197, 86]-NRT-code), using algebraic-geometric NRT-code AG(3;F,301P) [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
  - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
2. linear OOA(4¹⁶³, 129, F₄, 3, 58) (dual of [(129, 3), 224, 59]-NRT-code), using algebraic-geometric NRT-code AG(3;F,328P) [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130 (see above)
3. linear OOA(4³³, 20, F₄, 3, 26) (dual of [(20, 3), 27, 27]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4³³, 21, F₄, 3, 26) (dual of [(21, 3), 30, 27]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,36P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, 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.