MinT - Information on Result #908615

Information on Result #908615

Linear OOA(2²⁰⁹, 108, F₂, 2, 108) (dual of [(108, 2), 7, 109]-NRT-code), using juxtaposition based on

linear OOA(2²¹, 14, F₂, 2, 12) (dual of [(14, 2), 7, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2²¹, 15, F₂, 2, 12) (dual of [(15, 2), 9, 13]-NRT-code), using
  - extracting embedded OOA [i] based on digital (9, 21, 15)-net over F₂, using
    - linear code embedding found in a computer search [i]
linear OOA(2¹⁸¹, 94, F₂, 2, 95) (dual of [(94, 2), 7, 96]-NRT-code), using
- repeating each code word 2 times [i] based on linear OOA(2⁸⁷, 47, F₂, 2, 47) (dual of [(47, 2), 7, 48]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2⁴⁰, 23, F₂, 2, 23) (dual of [(23, 2), 6, 24]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(2¹⁷, 11, F₂, 2, 11) (dual of [(11, 2), 5, 12]-NRT-code), using
        (u,Â u+v)-construction [i] based on
        linear OOA(2⁶, 5, F₂, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,4P) [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(2¹¹, 6, F₂, 2, 11) (dual of [(6, 2), 1, 12]-NRT-code), using
        dual of repetition NRT-code with length 6 [i]
        linear OOA(2²³, 12, F₂, 2, 23) (dual of [(12, 2), 1, 24]-NRT-code), using
        dual of repetition NRT-code with length 12 [i]
    2. linear OOA(2⁴⁷, 24, F₂, 2, 47) (dual of [(24, 2), 1, 48]-NRT-code), using
      - dual of repetition NRT-code with length 24 [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.