MinT - Information on Result #2881513

Information on Result #2881513

Linear OOA(3²³¹, 86, F₃, 5, 103) (dual of [(86, 5), 199, 104]-NRT-code), using 3¹ times duplication based on linear OOA(3²³⁰, 86, F₃, 5, 103) (dual of [(86, 5), 200, 104]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3⁸², 38, F₃, 5, 51) (dual of [(38, 5), 108, 52]-NRT-code), using
  - constructionÂ X applied to AG(5;F,64P) âŠ‚ AG(5;F,67P) [i] based on
    1. linear OOA(3⁷⁷, 36, F₃, 5, 51) (dual of [(36, 5), 103, 52]-NRT-code), using algebraic-geometric NRT-code AG(5;F,64P) 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(3⁷¹, 36, F₃, 5, 45) (dual of [(36, 5), 109, 46]-NRT-code), using algebraic-geometric NRT-code AG(5;F,67P) 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(3¹⁴⁸, 48, F₃, 5, 103) (dual of [(48, 5), 92, 104]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(5;F,136P) [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.