MinT - Information on Result #2663504

Information on Result #2663504

Linear OOA(4²⁵³, 90, F₄, 3, 184) (dual of [(90, 3), 17, 185]-NRT-code), using 2 step truncation based on linear OOA(4²⁵⁵, 91, F₄, 3, 186) (dual of [(91, 3), 18, 187]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4⁸¹, 33, F₄, 3, 66) (dual of [(33, 3), 18, 67]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,32P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(4¹⁵⁶, 58, F₄, 3, 119) (dual of [(58, 3), 18, 120]-NRT-code), using
  - constructionÂ X applied to AG(3;F,45P) âŠ‚ AG(3;F,50P) [i] based on
    1. linear OOA(4¹⁵², 55, F₄, 3, 119) (dual of [(55, 3), 13, 120]-NRT-code), using algebraic-geometric NRT-code AG(3;F,45P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
    2. linear OOA(4¹⁴⁷, 55, F₄, 3, 114) (dual of [(55, 3), 18, 115]-NRT-code), using algebraic-geometric NRT-code AG(3;F,50P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
    3. linear OOA(4⁴, 3, F₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(4⁴, 4, F₄, 3, 4) (dual of [(4, 3), 8, 5]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(3;8,4) [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.