MinT - Information on Result #909217

Information on Result #909217

Linear OOA(3²¹³, 109, F₃, 2, 145) (dual of [(109, 2), 5, 146]-NRT-code), using juxtaposition based on

linear OOA(3³⁷, 21, F₃, 2, 27) (dual of [(21, 2), 5, 28]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹⁰, 7, F₃, 2, 9) (dual of [(7, 2), 4, 10]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;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(3¹³, 7, F₃, 2, 13) (dual of [(7, 2), 1, 14]-NRT-code), using
    - dual of repetition NRT-code with length 7 [i]
  3. linear OOA(3¹⁴, 7, F₃, 2, 14) (dual of [(7, 2), 0, 15]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
linear OOA(3¹⁷¹, 88, F₃, 2, 117) (dual of [(88, 2), 5, 118]-NRT-code), using
- juxtaposition [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(3¹⁴⁷, 76, F₃, 2, 101) (dual of [(76, 2), 5, 102]-NRT-code), using
    - repeating each code word 2 times [i] based on 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
        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 (see above)
        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]
        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.