MinT - Information on Result #2881613

Information on Result #2881613

Linear OOA(3²⁴⁰, 86, F₃, 5, 108) (dual of [(86, 5), 190, 109]-NRT-code), using 3² times duplication based on linear OOA(3²³⁸, 86, F₃, 5, 108) (dual of [(86, 5), 192, 109]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3⁸⁵, 38, F₃, 5, 54) (dual of [(38, 5), 105, 55]-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(3⁴, 2, F₃, 5, 4) (dual of [(2, 5), 6, 5]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(3⁴, 3, F₃, 5, 4) (dual of [(3, 5), 11, 5]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(5;11,3) [i]
2. linear OOA(3¹⁵³, 48, F₃, 5, 108) (dual of [(48, 5), 87, 109]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(5;F,131P) [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.