MinT - Information on Result #909210

Information on Result #909210

Linear OOA(3¹⁰⁷, 56, F₃, 2, 74) (dual of [(56, 2), 5, 75]-NRT-code), using juxtaposition based on

linear OOA(3³¹, 18, F₃, 2, 23) (dual of [(18, 2), 5, 24]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁸, 6, F₃, 2, 7) (dual of [(6, 2), 4, 8]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3⁸, 7, F₃, 2, 7) (dual of [(7, 2), 6, 8]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,6P) [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(3¹¹, 6, F₃, 2, 11) (dual of [(6, 2), 1, 12]-NRT-code), using
    - dual of repetition NRT-code with length 6 [i]
  3. linear OOA(3¹², 6, F₃, 2, 12) (dual of [(6, 2), 0, 13]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
linear OOA(3⁷¹, 38, F₃, 2, 50) (dual of [(38, 2), 5, 51]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(3²⁰, 12, F₃, 2, 16) (dual of [(12, 2), 4, 17]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,7P) [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.