MinT - Information on Result #2689740

Information on Result #2689740

Linear OOA(4¹²³, 147, F₄, 3, 42) (dual of [(147, 3), 318, 43]-NRT-code), using 4¹ times duplication based on linear OOA(4¹²², 147, F₄, 3, 42) (dual of [(147, 3), 319, 43]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(4²⁶, 17, F₄, 3, 21) (dual of [(17, 3), 25, 22]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,29P) [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(4⁹⁶, 130, F₄, 3, 42) (dual of [(130, 3), 294, 43]-NRT-code), using
  - extracting embedded OOA [i] based on digital (54, 96, 130)-net over F₄, using
    - trace code for nets [i] based on digital (6, 48, 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.