MinT - Information on Result #2681372

Information on Result #2681372

Linear OOA(3¹²⁴, 57, F₃, 3, 62) (dual of [(57, 3), 47, 63]-NRT-code), using 3¹ times duplication based on linear OOA(3¹²³, 57, F₃, 3, 62) (dual of [(57, 3), 48, 63]-NRT-code), using

strength reduction [i] based on linear OOA(3¹²³, 57, F₃, 3, 63) (dual of [(57, 3), 48, 64]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(9³³, 19, F₉, 3, 31) (dual of [(19, 3), 24, 32]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9³³, 20, F₉, 3, 31) (dual of [(20, 3), 27, 32]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,28P) [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.