MinT - Information on Result #1058687

Information on Result #1058687

Linear OOA(2²¹², 57, F₂, 4, 110) (dual of [(57, 4), 16, 111]-NRT-code), using OOA 2-folding based on linear OOA(2²¹², 114, F₂, 2, 110) (dual of [(114, 2), 16, 111]-NRT-code), using

2 step truncation [i] based on linear OOA(2²¹⁴, 115, F₂, 2, 112) (dual of [(115, 2), 16, 113]-NRT-code), using
- strength reduction [i] based on linear OOA(2²¹⁴, 115, F₂, 2, 113) (dual of [(115, 2), 16, 114]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OA(16¹⁹, 23, F₁₆, 18) (dual of [23, 4, 19]-code), using
      - discarding factors / shortening the dual code based on linear OA(16¹⁹, 24, F₁₆, 18) (dual of [24, 5, 19]-code), using
        extended algebraic-geometric code AG_e(F,5P) [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 OOA(2⁶, 5, F₂, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [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.