MinT - Information on Result #909788

Information on Result #909788

Linear OOA(4²⁵³, 129, F₄, 2, 193) (dual of [(129, 2), 5, 194]-NRT-code), using juxtaposition based on

linear OOA(4⁵⁹, 32, F₄, 2, 47) (dual of [(32, 2), 5, 48]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4¹², 8, F₄, 2, 11) (dual of [(8, 2), 4, 12]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4¹², 9, F₄, 2, 11) (dual of [(9, 2), 6, 12]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,6P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
        the Hermitian function field over F₄ [i]
  2. linear OOA(4¹⁵, 8, F₄, 2, 15) (dual of [(8, 2), 1, 16]-NRT-code), using
    - dual of repetition NRT-code with length 8 [i]
  3. linear OOA(4¹⁶, 8, F₄, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  4. linear OOA(4¹⁶, 8, F₄, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code) (see above)
linear OOA(4¹⁸⁹, 97, F₄, 2, 145) (dual of [(97, 2), 5, 146]-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, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(4¹⁶¹, 83, F₄, 2, 124) (dual of [(83, 2), 5, 125]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(4²³, 14, F₄, 2, 20) (dual of [(14, 2), 5, 21]-NRT-code) (see above)
      2. linear OOA(4¹³³, 69, F₄, 2, 103) (dual of [(69, 2), 5, 104]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(4²³, 14, F₄, 2, 20) (dual of [(14, 2), 5, 21]-NRT-code) (see above)
        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.