MinT - Information on Result #2963672

Information on Result #2963672

Linear OOA(2²⁵⁴, 272, F₂, 7, 49) (dual of [(272, 7), 1650, 50]-NRT-code), using 2¹ times duplication based on linear OOA(2²⁵³, 272, F₂, 7, 49) (dual of [(272, 7), 1651, 50]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2³³, 12, F₂, 7, 24) (dual of [(12, 7), 51, 25]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(7;F,59P) [i] based on function field F/F₂ with g(F) = 9 and N(F) ≥ 12, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2²²⁰, 260, F₂, 7, 49) (dual of [(260, 7), 1600, 50]-NRT-code), using
  - extracting embedded OOA [i] based on digital (171, 220, 260)-net over F₂, using
    - trace code for nets [i] based on digital (6, 55, 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.