MinT - Information on Result #2654436

Information on Result #2654436

Linear OOA(2¹³¹, 53, F₂, 3, 64) (dual of [(53, 3), 28, 65]-NRT-code), using 1 step truncation based on linear OOA(2¹³², 54, F₂, 3, 65) (dual of [(54, 3), 30, 66]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4³⁹, 18, F₄, 3, 32) (dual of [(18, 3), 15, 33]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4³⁹, 21, F₄, 3, 32) (dual of [(21, 3), 24, 33]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,30P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, 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.