MinT - Information on Result #2637296

Information on Result #2637296

Linear OOA(4²³⁹, 82, F₄, 3, 189) (dual of [(82, 3), 7, 190]-NRT-code), using strength reduction based on linear OOA(4²³⁹, 82, F₄, 3, 195) (dual of [(82, 3), 7, 196]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4³⁵, 14, F₄, 3, 32) (dual of [(14, 3), 7, 33]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,9P) [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(4¹⁹⁷, 68, F₄, 3, 162) (dual of [(68, 3), 7, 163]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(4³⁵, 14, F₄, 3, 32) (dual of [(14, 3), 7, 33]-NRT-code) (see above)
    2. linear OOA(4¹⁵⁵, 54, F₄, 3, 129) (dual of [(54, 3), 7, 130]-NRT-code), using
      - repeating each code word 2 times [i] based on linear OOA(4⁷⁴, 27, F₄, 3, 64) (dual of [(27, 3), 7, 65]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,16P) [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, 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.