MinT - Information on Result #2670677

Information on Result #2670677

Linear OOA(2¹⁰⁸, 45, F₂, 3, 54) (dual of [(45, 3), 27, 55]-NRT-code), using 2¹ times duplication based on linear OOA(2¹⁰⁷, 45, F₂, 3, 54) (dual of [(45, 3), 28, 55]-NRT-code), using

strength reduction [i] based on linear OOA(2¹⁰⁷, 45, F₂, 3, 55) (dual of [(45, 3), 28, 56]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(4³¹, 15, F₄, 3, 27) (dual of [(15, 3), 14, 28]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,17P) [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
      - an explicitly constructive algebraic function field [i]
  2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 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.