MinT - Information on Result #2673353

Information on Result #2673353

Linear OOA(2¹⁹⁹, 85, F₂, 3, 88) (dual of [(85, 3), 56, 89]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹⁹⁶, 84, F₂, 3, 88) (dual of [(84, 3), 56, 89]-NRT-code), using

strength reduction [i] based on linear OOA(2¹⁹⁶, 84, F₂, 3, 89) (dual of [(84, 3), 56, 90]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(4⁵⁶, 28, F₄, 3, 44) (dual of [(28, 3), 28, 45]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,39P) [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 28, 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.