MinT - Information on Result #1054628

Information on Result #1054628

Linear OOA(2¹³⁰, 57, F₂, 4, 41) (dual of [(57, 4), 98, 42]-NRT-code), using OOA 2-folding based on linear OOA(2¹³⁰, 114, F₂, 2, 41) (dual of [(114, 2), 98, 42]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹³⁰, 115, F₂, 2, 41) (dual of [(115, 2), 100, 42]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(16²¹, 23, F₁₆, 2, 20) (dual of [(23, 2), 25, 21]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16²¹, 24, F₁₆, 2, 20) (dual of [(24, 2), 27, 21]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,27P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
        a function field by SÃ©mirat [i]
  2. linear OA(2¹, 5, F₂, 1) (dual of [5, 4, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 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.