MinT - Information on Result #908588

Information on Result #908588

Linear OOA(2²²⁷, 117, F₂, 2, 117) (dual of [(117, 2), 7, 118]-NRT-code), using juxtaposition based on

linear OOA(2⁷, 7, F₂, 2, 5) (dual of [(7, 2), 7, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (2, 7, 7)-net over F₂, using
  - a shift-net [i]
linear OOA(2²¹³, 110, F₂, 2, 111) (dual of [(110, 2), 7, 112]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁰², 54, F₂, 2, 55) (dual of [(54, 2), 6, 56]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2⁴⁷, 26, F₂, 2, 27) (dual of [(26, 2), 5, 28]-NRT-code), using
        (u,Â u+v)-construction [i] based on
        linear OOA(2²⁰, 12, F₂, 2, 13) (dual of [(12, 2), 4, 14]-NRT-code), using
        (u,Â u+v)-construction [i] based on
        linear OOA(2⁷, 5, F₂, 2, 6) (dual of [(5, 2), 3, 7]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,3P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]
        linear OOA(2¹³, 7, F₂, 2, 13) (dual of [(7, 2), 1, 14]-NRT-code), using
        dual of repetition NRT-code with length 7 [i]
        linear OOA(2²⁷, 14, F₂, 2, 27) (dual of [(14, 2), 1, 28]-NRT-code), using
        dual of repetition NRT-code with length 14 [i]
      2. linear OOA(2⁵⁵, 28, F₂, 2, 55) (dual of [(28, 2), 1, 56]-NRT-code), using
        dual of repetition NRT-code with length 28 [i]
  2. linear OOA(2¹¹¹, 56, F₂, 2, 111) (dual of [(56, 2), 1, 112]-NRT-code), using
    - dual of repetition NRT-code with length 56 [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.