MinT - Information on Result #1133644

Information on Result #1133644

Linear OOA(2⁸⁰, 16, F₂, 6, 42) (dual of [(16, 6), 16, 43]-NRT-code), using OOA 2-folding based on linear OOA(2⁸⁰, 32, F₂, 3, 42) (dual of [(32, 3), 16, 43]-NRT-code), using

1 step truncation [i] based on linear OOA(2⁸¹, 33, F₂, 3, 43) (dual of [(33, 3), 18, 44]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(4²⁴, 11, F₄, 3, 21) (dual of [(11, 3), 9, 22]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4²⁴, 14, F₄, 3, 21) (dual of [(14, 3), 18, 22]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,20P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, 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.