MinT - Information on Result #2682954

Information on Result #2682954

Linear OOA(3¹⁶², 69, F₃, 3, 86) (dual of [(69, 3), 45, 87]-NRT-code), using 3¹ times duplication based on linear OOA(3¹⁶¹, 69, F₃, 3, 86) (dual of [(69, 3), 46, 87]-NRT-code), using

strength reduction [i] based on linear OOA(3¹⁶¹, 69, F₃, 3, 87) (dual of [(69, 3), 46, 88]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(9⁴⁶, 23, F₉, 3, 43) (dual of [(23, 3), 23, 44]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9⁴⁶, 28, F₉, 3, 43) (dual of [(28, 3), 38, 44]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,40P) [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
        the Hermitian function field over F₉ [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.