MinT - Information on Result #2805866

Information on Result #2805866

Linear OOA(3²¹⁵, 78, F₃, 4, 101) (dual of [(78, 4), 97, 102]-NRT-code), using 3¹ times duplication based on linear OOA(3²¹⁴, 78, F₃, 4, 101) (dual of [(78, 4), 98, 102]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3⁷⁷, 37, F₃, 4, 50) (dual of [(37, 4), 71, 51]-NRT-code), using
  - extracting embedded OOA [i] based on digital (27, 77, 37)-net over F₃, using
    - net from sequence [i] based on digital (27, 36)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 26, N(F)Â =Â 36, and 1 place with degree 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(3¹³⁷, 41, F₃, 4, 101) (dual of [(41, 4), 27, 102]-NRT-code), using
  - constructionÂ X applied to AG(4;F,21P) âŠ‚ AG(4;F,26P) [i] based on
    1. linear OOA(3¹²⁷, 36, F₃, 4, 101) (dual of [(36, 4), 17, 102]-NRT-code), using algebraic-geometric NRT-code AG(4;F,21P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
    2. linear OOA(3¹¹⁷, 36, F₃, 4, 91) (dual of [(36, 4), 27, 92]-NRT-code), using algebraic-geometric NRT-code AG(4;F,26P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
    3. linear OOA(3¹⁰, 5, F₃, 4, 9) (dual of [(5, 4), 10, 10]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(3¹⁰, 7, F₃, 4, 9) (dual of [(7, 4), 18, 10]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,18P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, 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.