MinT - Information on Result #858941

Information on Result #858941

Linear OOA(16⁵⁹, 33, F₁₆, 2, 52) (dual of [(33, 2), 7, 53]-NRT-code), using OOA 2-folding based on linear OA(16⁵⁹, 66, F₁₆, 52) (dual of [66, 7, 53]-code), using

discarding factors / shortening the dual code based on linear OA(16⁵⁹, 67, F₁₆, 52) (dual of [67, 8, 53]-code), using
- constructionÂ X applied to AG(F,11P) âŠ‚ AG(F,13P) [i] based on
  1. linear OA(16⁵⁸, 64, F₁₆, 52) (dual of [64, 6, 53]-code), using algebraic-geometric code AG(F,11P) [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(16⁵⁶, 64, F₁₆, 50) (dual of [64, 8, 51]-code), using algebraic-geometric code AG(F,13P) [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.