MinT - Information on Result #1062476

Information on Result #1062476

Linear OOA(3⁷⁸, 27, F₃, 4, 38) (dual of [(27, 4), 30, 39]-NRT-code), using OOA 2-folding based on linear OOA(3⁷⁸, 54, F₃, 2, 38) (dual of [(54, 2), 30, 39]-NRT-code), using

strength reduction [i] based on linear OOA(3⁷⁸, 54, F₃, 2, 39) (dual of [(54, 2), 30, 40]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(9²¹, 18, F₉, 2, 19) (dual of [(18, 2), 15, 20]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9²¹, 20, F₉, 2, 19) (dual of [(20, 2), 19, 20]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,20P) [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
        a function field by GarcÃa and Quoos [i]
  2. linear OA(3¹, 3, F₃, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [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.