MinT - Information on Result #2693286

Information on Result #2693286

Linear OOA(4²²⁴, 165, F₄, 3, 77) (dual of [(165, 3), 271, 78]-NRT-code), using 4¹ times duplication based on linear OOA(4²²³, 165, F₄, 3, 77) (dual of [(165, 3), 272, 78]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(4⁵⁷, 35, F₄, 3, 38) (dual of [(35, 3), 48, 39]-NRT-code), using
  - constructionÂ X applied to AG(3;F,57P) âŠ‚ AG(3;F,62P) [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(4⁴⁸, 32, F₄, 3, 33) (dual of [(32, 3), 48, 34]-NRT-code), using algebraic-geometric NRT-code AG(3;F,62P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33 (see above)
    3. linear OOA(4⁴, 3, F₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(4⁴, 4, F₄, 3, 4) (dual of [(4, 3), 8, 5]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(3;8,4) [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.