MinT - Information on Result #909795

Information on Result #909795

Linear OOA(4²³⁷, 121, F₄, 2, 181) (dual of [(121, 2), 5, 182]-NRT-code), using juxtaposition based on

linear OOA(4⁹⁹, 52, F₄, 2, 77) (dual of [(52, 2), 5, 78]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4²², 13, F₄, 2, 19) (dual of [(13, 2), 4, 20]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4²², 14, F₄, 2, 19) (dual of [(14, 2), 6, 20]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,8P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
        an explicitly constructive algebraic function field [i]
  2. linear OOA(4²⁵, 13, F₄, 2, 25) (dual of [(13, 2), 1, 26]-NRT-code), using
    - dual of repetition NRT-code with length 13 [i]
  3. linear OOA(4²⁶, 13, F₄, 2, 26) (dual of [(13, 2), 0, 27]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  4. linear OOA(4²⁶, 13, F₄, 2, 26) (dual of [(13, 2), 0, 27]-NRT-code) (see above)
linear OOA(4¹³³, 69, F₄, 2, 103) (dual of [(69, 2), 5, 104]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(4²³, 14, F₄, 2, 20) (dual of [(14, 2), 5, 21]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,7P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14 (see above)
  2. linear OOA(4¹⁰⁵, 55, F₄, 2, 82) (dual of [(55, 2), 5, 83]-NRT-code), using
    - 1 step truncation [i] based on linear OOA(4¹⁰⁶, 56, F₄, 2, 83) (dual of [(56, 2), 6, 84]-NRT-code), using
      - generalized (u,Â u+v)-construction [i] based on
        linear OOA(4²³, 14, F₄, 2, 20) (dual of [(14, 2), 5, 21]-NRT-code) (see above)
        linear OOA(4²⁷, 14, F₄, 2, 27) (dual of [(14, 2), 1, 28]-NRT-code), using
        dual of repetition NRT-code with length 14 [i]
        linear OOA(4²⁸, 14, F₄, 2, 28) (dual of [(14, 2), 0, 29]-NRT-code), using
        complete OOA / dual of NRT-code with only one code word [i]
        linear OOA(4²⁸, 14, F₄, 2, 28) (dual of [(14, 2), 0, 29]-NRT-code) (see above)

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.