MinT - Information on Result #2468226

Information on Result #2468226

Linear OOA(4⁵⁷, 31, F₄, 2, 44) (dual of [(31, 2), 5, 45]-NRT-code), using 2 step truncation based on linear OOA(4⁵⁹, 32, F₄, 2, 46) (dual of [(32, 2), 5, 47]-NRT-code), using

strength reduction [i] 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)

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.