MinT - Information on Result #2632664

Information on Result #2632664

Linear OOA(4¹⁶⁷, 57, F₄, 3, 138) (dual of [(57, 3), 4, 139]-NRT-code), using strength reduction based on linear OOA(4¹⁶⁷, 57, F₄, 3, 144) (dual of [(57, 3), 4, 145]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4²⁰, 8, F₄, 3, 19) (dual of [(8, 3), 4, 20]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4²⁰, 9, F₄, 3, 19) (dual of [(9, 3), 7, 20]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,7P) [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(4¹⁴³, 49, F₄, 3, 124) (dual of [(49, 3), 4, 125]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(4¹⁷, 7, F₄, 3, 16) (dual of [(7, 3), 4, 17]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(4¹⁷, 9, F₄, 3, 16) (dual of [(9, 3), 10, 17]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,10P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9 (see above)
    2. linear OOA(4¹²², 42, F₄, 3, 107) (dual of [(42, 3), 4, 108]-NRT-code), using
      - repeating each code word 3 times [i] based on linear OOA(4³⁸, 14, F₄, 3, 35) (dual of [(14, 3), 4, 36]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,6P) [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.