MinT - Information on Result #2858164

Information on Result #2858164

Linear OOA(3²⁴², 86, F₃, 5, 110) (dual of [(86, 5), 188, 111]-NRT-code), using strength reduction based on linear OOA(3²⁴², 86, F₃, 5, 111) (dual of [(86, 5), 188, 112]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3⁸⁶, 38, F₃, 5, 55) (dual of [(38, 5), 104, 56]-NRT-code), using
  - constructionÂ X applied to AG(5;F,62P) âŠ‚ AG(5;F,65P) [i] based on
    1. linear OOA(3⁸¹, 36, F₃, 5, 55) (dual of [(36, 5), 99, 56]-NRT-code), using algebraic-geometric NRT-code AG(5;F,62P) 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(3⁷⁵, 36, F₃, 5, 49) (dual of [(36, 5), 105, 50]-NRT-code), using algebraic-geometric NRT-code AG(5;F,65P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
    3. linear OOA(3⁵, 2, F₃, 5, 5) (dual of [(2, 5), 5, 6]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(3⁵, 3, F₃, 5, 5) (dual of [(3, 5), 10, 6]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(5;10,3) [i]
2. linear OOA(3¹⁵⁶, 48, F₃, 5, 111) (dual of [(48, 5), 84, 112]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(5;F,128P) [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, 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.