MinT - Information on Result #2625035

Information on Result #2625035

Linear OOA(3¹⁸⁴, 66, F₃, 3, 126) (dual of [(66, 3), 14, 127]-NRT-code), using strength reduction based on linear OOA(3¹⁸⁴, 66, F₃, 3, 127) (dual of [(66, 3), 14, 128]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(3⁷⁰, 28, F₃, 3, 55) (dual of [(28, 3), 14, 56]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,28P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(3¹⁰⁰, 38, F₃, 3, 71) (dual of [(38, 3), 14, 72]-NRT-code), using
  - constructionÂ X applied to AG(3;F,18P) âŠ‚ AG(3;F,20P) [i] based on
    1. linear OOA(3⁹⁷, 36, F₃, 3, 71) (dual of [(36, 3), 11, 72]-NRT-code), using algebraic-geometric NRT-code AG(3;F,18P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
    2. linear OOA(3⁹³, 36, F₃, 3, 67) (dual of [(36, 3), 15, 68]-NRT-code), using algebraic-geometric NRT-code AG(3;F,20P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
    3. linear OOA(3³, 2, F₃, 3, 3) (dual of [(2, 3), 3, 4]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(3³, 3, F₃, 3, 3) (dual of [(3, 3), 6, 4]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(3;6,3) [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.