MinT - Information on Result #806623

Information on Result #806623

Linear OOA(2⁶⁸, 52, F₂, 2, 22) (dual of [(52, 2), 36, 23]-NRT-code), using OOA 2-folding based on linear OA(2⁶⁸, 104, F₂, 22) (dual of [104, 36, 23]-code), using

1 times truncation [i] based on linear OA(2⁶⁹, 105, F₂, 23) (dual of [105, 36, 24]-code), using
- concatenation of two codes [i] based on
  1. linear OA(16¹², 21, F₁₆, 11) (dual of [21, 9, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(16¹², 24, F₁₆, 11) (dual of [24, 12, 12]-code), using
      - extended algebraic-geometric code AG_e(F,12P) [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.