MinT - Information on Result #2843601

Information on Result #2843601

Linear OOA(2¹⁹³, 76, F₂, 5, 64) (dual of [(76, 5), 187, 65]-NRT-code), using strength reduction based on linear OOA(2¹⁹³, 76, F₂, 5, 65) (dual of [(76, 5), 187, 66]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁷⁴, 34, F₂, 5, 32) (dual of [(34, 5), 96, 33]-NRT-code), using
  - extracting embedded OOA [i] based on digital (42, 74, 34)-net over F₂, using
    - trace code for nets [i] based on digital (5, 37, 17)-net over F₄, using
      - net from sequence [i] based on digital (5, 16)-sequence over F₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [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(2¹¹⁹, 42, F₂, 5, 65) (dual of [(42, 5), 91, 66]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(5;F,144P) [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
    - an explicitly constructive algebraic function field [i]
  - algebraic-geometric NRT-code AG(5;F,24P) with degPÂ =Â 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, 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.