MinT - Information on Result #824100

Information on Result #824100

Linear OOA(4⁶⁴, 67, F₄, 2, 25) (dual of [(67, 2), 70, 26]-NRT-code), using OOA 2-folding based on linear OA(4⁶⁴, 134, F₄, 25) (dual of [134, 70, 26]-code), using

trace code [i] based on linear OA(16³², 67, F₁₆, 25) (dual of [67, 35, 26]-code), using
- constructionÂ X applied to AG(F,38P) âŠ‚ AG(F,40P) [i] based on
  1. linear OA(16³¹, 64, F₁₆, 25) (dual of [64, 33, 26]-code), using algebraic-geometric code AG(F,38P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]
  2. linear OA(16²⁹, 64, F₁₆, 23) (dual of [64, 35, 24]-code), using algebraic-geometric code AG(F,40P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16¹, 3, F₁₆, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(16¹, s, F₁₆, 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.