MinT - Information on Result #2663331

Information on Result #2663331

Linear OOA(4¹⁸⁵, 67, F₄, 3, 136) (dual of [(67, 3), 16, 137]-NRT-code), using 3 step truncation based on linear OOA(4¹⁸⁸, 68, F₄, 3, 139) (dual of [(68, 3), 16, 140]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4⁸³, 33, F₄, 3, 68) (dual of [(33, 3), 16, 69]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,30P) [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(4⁸⁹, 35, F₄, 3, 70) (dual of [(35, 3), 16, 71]-NRT-code), using
  - constructionÂ X applied to AG(3;F,25P) âŠ‚ AG(3;F,30P) [i] based on
    1. linear OOA(4⁸⁵, 32, F₄, 3, 70) (dual of [(32, 3), 11, 71]-NRT-code), using algebraic-geometric NRT-code AG(3;F,25P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33 (see above)
    2. linear OOA(4⁸⁰, 32, F₄, 3, 65) (dual of [(32, 3), 16, 66]-NRT-code), using algebraic-geometric NRT-code AG(3;F,30P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33 (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.