MinT - Information on Result #1057507

Information on Result #1057507

Linear OOA(2²³³, 89, F₂, 4, 78) (dual of [(89, 4), 123, 79]-NRT-code), using OOA 2-folding based on linear OOA(2²³³, 178, F₂, 2, 78) (dual of [(178, 2), 123, 79]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²³³, 179, F₂, 2, 78) (dual of [(179, 2), 125, 79]-NRT-code), using
- 1 step truncation [i] based on linear OOA(2²³⁴, 180, F₂, 2, 79) (dual of [(180, 2), 126, 80]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OOA(8⁴⁸, 45, F₈, 2, 39) (dual of [(45, 2), 42, 40]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,50P) [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
        an explicitly constructive algebraic function field [i]
    2. linear OA(2¹, 4, F₂, 1) (dual of [4, 3, 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.