MinT - Information on Result #909128

Information on Result #909128

Linear OOA(3¹⁹⁰, 98, F₃, 2, 127) (dual of [(98, 2), 6, 128]-NRT-code), using juxtaposition based on

linear OOA(3²⁰, 13, F₃, 2, 15) (dual of [(13, 2), 6, 16]-NRT-code), using
- extracting embedded OOA [i] based on digital (5, 20, 13)-net over F₃, using
  - net from sequence [i] based on digital (5, 12)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 4, N(F)Â =Â 12, and 1 place with degree 2 [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using an explicitly constructive algebraic function field [i]
linear OOA(3¹⁶⁴, 85, F₃, 2, 111) (dual of [(85, 2), 6, 112]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(3²⁰, 13, F₃, 2, 15) (dual of [(13, 2), 6, 16]-NRT-code) (see above)
  2. linear OOA(3¹³⁸, 72, F₃, 2, 95) (dual of [(72, 2), 6, 96]-NRT-code), using
    - repeating each code word 2 times [i] based on linear OOA(3⁶⁶, 36, F₃, 2, 47) (dual of [(36, 2), 6, 48]-NRT-code), using
      - generalized (u,Â u+v)-construction [i] based on
        linear OOA(3¹⁹, 12, F₃, 2, 15) (dual of [(12, 2), 5, 16]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,8P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12 (see above)
        linear OOA(3²³, 12, F₃, 2, 23) (dual of [(12, 2), 1, 24]-NRT-code), using
        dual of repetition NRT-code with length 12 [i]
        linear OOA(3²⁴, 12, F₃, 2, 24) (dual of [(12, 2), 0, 25]-NRT-code), using
        complete OOA / dual of NRT-code with only one code word [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.