MinT - Information on Result #2693045

Information on Result #2693045

Linear OOA(4²¹¹, 160, F₄, 3, 74) (dual of [(160, 3), 269, 75]-NRT-code), using 4¹ times duplication based on linear OOA(4²¹⁰, 160, F₄, 3, 74) (dual of [(160, 3), 270, 75]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(4⁵⁰, 30, F₄, 3, 37) (dual of [(30, 3), 40, 38]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,52P) [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
    - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
2. linear OOA(4¹⁶⁰, 130, F₄, 3, 74) (dual of [(130, 3), 230, 75]-NRT-code), using
  - extracting embedded OOA [i] based on digital (86, 160, 130)-net over F₄, using
    - trace code for nets [i] based on digital (6, 80, 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.