MinT - Information on Result #2792489

Information on Result #2792489

Linear OOA(2¹⁶⁹, 74, F₂, 4, 54) (dual of [(74, 4), 127, 55]-NRT-code), using 2¹ times duplication based on linear OOA(2¹⁶⁸, 74, F₂, 4, 54) (dual of [(74, 4), 128, 55]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2³⁰, 8, F₂, 4, 27) (dual of [(8, 4), 2, 28]-NRT-code), using
  - repeating each code word 4 times [i] based on linear OOA(2⁶, 2, F₂, 4, 6) (dual of [(2, 4), 2, 7]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(4;2,2) [i]
2. linear OOA(2¹³⁸, 66, F₂, 4, 54) (dual of [(66, 4), 126, 55]-NRT-code), using
  - extracting embedded OOA [i] based on digital (84, 138, 66)-net over F₂, using
    - trace code for nets [i] based on digital (15, 69, 33)-net over F₄, using
      - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, 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.