MinT - Information on Result #2674126

Information on Result #2674126

Linear OOA(2²²³, 90, F₂, 3, 106) (dual of [(90, 3), 47, 107]-NRT-code), using 2¹ times duplication based on linear OOA(2²²², 90, F₂, 3, 106) (dual of [(90, 3), 48, 107]-NRT-code), using

strength reduction [i] based on linear OOA(2²²², 90, F₂, 3, 107) (dual of [(90, 3), 48, 108]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(4⁶⁶, 30, F₄, 3, 53) (dual of [(30, 3), 24, 54]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,36P) [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
      - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [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.