MinT - Information on Result #2632747

Information on Result #2632747

Linear OOA(4¹⁶⁹, 58, F₄, 3, 140) (dual of [(58, 3), 5, 141]-NRT-code), using strength reduction based on linear OOA(4¹⁶⁹, 58, F₄, 3, 142) (dual of [(58, 3), 5, 143]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4¹⁹, 8, F₄, 3, 18) (dual of [(8, 3), 5, 19]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4¹⁹, 9, F₄, 3, 18) (dual of [(9, 3), 8, 19]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,8P) [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(4¹⁴⁵, 50, F₄, 3, 123) (dual of [(50, 3), 5, 124]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(4¹⁹, 8, F₄, 3, 18) (dual of [(8, 3), 5, 19]-NRT-code) (see above)
    2. linear OOA(4¹²¹, 42, F₄, 3, 104) (dual of [(42, 3), 5, 105]-NRT-code), using
      - repeating each code word 3 times [i] based on linear OOA(4³⁷, 14, F₄, 3, 34) (dual of [(14, 3), 5, 35]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;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]

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.