MinT - Information on Result #2693288

Information on Result #2693288

Linear OOA(4²²⁹, 168, F₄, 3, 77) (dual of [(168, 3), 275, 78]-NRT-code), using 4¹ times duplication based on linear OOA(4²²⁸, 168, F₄, 3, 77) (dual of [(168, 3), 276, 78]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(4⁶², 38, F₄, 3, 38) (dual of [(38, 3), 52, 39]-NRT-code), using
  - constructionÂ X applied to AG(3;F,57P) âŠ‚ AG(3;F,66P) [i] based on
    1. linear OOA(4⁵³, 32, F₄, 3, 38) (dual of [(32, 3), 43, 39]-NRT-code), using algebraic-geometric NRT-code AG(3;F,57P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]
    2. linear OOA(4⁴⁴, 32, F₄, 3, 29) (dual of [(32, 3), 52, 30]-NRT-code), using algebraic-geometric NRT-code AG(3;F,66P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33 (see above)
    3. linear OOA(4⁹, 6, F₄, 3, 8) (dual of [(6, 3), 9, 9]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(4⁹, 9, F₄, 3, 8) (dual of [(9, 3), 18, 9]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,18P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
        the Hermitian function field over F₄ [i]
2. linear OOA(4¹⁶⁶, 130, F₄, 3, 77) (dual of [(130, 3), 224, 78]-NRT-code), using
  - extracting embedded OOA [i] based on digital (89, 166, 130)-net over F₄, using
    - trace code for nets [i] based on digital (6, 83, 65)-net over F₁₆, using
      - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [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.