MinT - Information on Result #2626200

Information on Result #2626200

Linear OOA(3²⁰³, 69, F₃, 3, 158) (dual of [(69, 3), 4, 159]-NRT-code), using strength reduction based on linear OOA(3²⁰³, 69, F₃, 3, 168) (dual of [(69, 3), 4, 169]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(3²⁰, 8, F₃, 3, 18) (dual of [(8, 3), 4, 19]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,5P) [i] based on function field F/F₃ with g(F) = 2 and N(F) ≥ 8, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(3¹⁷⁹, 61, F₃, 3, 149) (dual of [(61, 3), 4, 150]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(3¹⁷, 7, F₃, 3, 16) (dual of [(7, 3), 4, 17]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,4P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(3¹⁵⁸, 54, F₃, 3, 132) (dual of [(54, 3), 4, 133]-NRT-code), using
      - juxtaposition [i] based on
        linear OOA(3¹⁷, 7, F₃, 3, 16) (dual of [(7, 3), 4, 17]-NRT-code) (see above)
        linear OOA(3¹³⁷, 47, F₃, 3, 115) (dual of [(47, 3), 4, 116]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(3¹⁷, 7, F₃, 3, 16) (dual of [(7, 3), 4, 17]-NRT-code) (see above)
        linear OOA(3¹¹⁶, 40, F₃, 3, 98) (dual of [(40, 3), 4, 99]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(9⁸, 10, F₉, 8) (dual of [10, 2, 9]-code or 10-arc in PG(7,9)), using
        extended Reedâ€“Solomon code RS_e(2,9) [i]
        Simplex code S(2,9) [i]
        linear OOA(3¹⁰, 4, F₃, 3, 10) (dual of [(4, 3), 2, 11]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;2,3) [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.