MinT - Information on Result #956630

Information on Result #956630

Linear OOA(3¹³⁰, 57, F₃, 3, 55) (dual of [(57, 3), 41, 56]-NRT-code), using OOA 3-folding based on linear OA(3¹³⁰, 171, F₃, 55) (dual of [171, 41, 56]-code), using

discarding factors / shortening the dual code based on linear OA(3¹³⁰, 172, F₃, 55) (dual of [172, 42, 56]-code), using
- concatenation of two codes [i] based on
  1. linear OA(27²⁹, 43, F₂₇, 27) (dual of [43, 14, 28]-code), using
    - discarding factors / shortening the dual code based on linear OA(27²⁹, 48, F₂₇, 27) (dual of [48, 19, 28]-code), using
      - extended algebraic-geometric code AG_e(F,20P) [i] based on function field F/F₂₇ with g(F) = 2 and N(F) ≥ 48, using
        a function field by GarcÃa and Quoos [i]
  2. linear OA(3¹, 4, F₃, 1) (dual of [4, 3, 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.