MinT - Information on Result #909156

Information on Result #909156

Linear OOA(3²¹⁴, 110, F₃, 2, 144) (dual of [(110, 2), 6, 145]-NRT-code), using juxtaposition 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
  1. 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, using
      - an explicitly constructive algebraic function field [i]
  2. 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]
  3. 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]
linear OOA(3¹⁴², 74, F₃, 2, 96) (dual of [(74, 2), 6, 97]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(3⁶⁴, 35, F₃, 2, 45) (dual of [(35, 2), 6, 46]-NRT-code), using
    - 10 step truncation [i] based on linear OOA(3⁷⁴, 40, F₃, 2, 55) (dual of [(40, 2), 6, 56]-NRT-code), using
      - concatenation of two NRT-codes [i] based on
        linear OA(9⁷, 10, F₉, 7) (dual of [10, 3, 8]-code or 10-arc in PG(6,9)), using
        extended Reedâ€“Solomon code RS_e(3,9) [i]
        linear OOA(3⁶, 4, F₃, 2, 6) (dual of [(4, 2), 2, 7]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;2,3) [i]
  2. linear OOA(3⁷², 39, F₃, 2, 50) (dual of [(39, 2), 6, 51]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(3²¹, 13, F₃, 2, 16) (dual of [(13, 2), 5, 17]-NRT-code), using
        extracting embedded OOA [i] based on digital (5, 21, 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]
      2. linear OOA(3²⁵, 13, F₃, 2, 25) (dual of [(13, 2), 1, 26]-NRT-code), using
        dual of repetition NRT-code with length 13 [i]
      3. linear OOA(3²⁶, 13, F₃, 2, 26) (dual of [(13, 2), 0, 27]-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.