MinT - Information on Result #2634822

Information on Result #2634822

Linear OOA(4²⁰⁷, 71, F₄, 3, 166) (dual of [(71, 3), 6, 167]-NRT-code), using strength reduction based on linear OOA(4²⁰⁷, 71, F₄, 3, 170) (dual of [(71, 3), 6, 171]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4¹⁸, 8, F₄, 3, 17) (dual of [(8, 3), 6, 18]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4¹⁸, 9, F₄, 3, 17) (dual of [(9, 3), 9, 18]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,9P) [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(4¹⁸³, 63, F₄, 3, 152) (dual of [(63, 3), 6, 153]-NRT-code), using
  - repeating each code word 3 times [i] based on linear OOA(4⁵⁷, 21, F₄, 3, 50) (dual of [(21, 3), 6, 51]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,12P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, 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.