MinT - Information on Result #860311

Information on Result #860311

Linear OOA(16¹²⁴, 113, F₁₆, 2, 83) (dual of [(113, 2), 102, 84]-NRT-code), using OOA 2-folding based on linear OA(16¹²⁴, 226, F₁₆, 83) (dual of [226, 102, 84]-code), using

discarding factors / shortening the dual code based on linear OA(16¹²⁴, 227, F₁₆, 83) (dual of [227, 103, 84]-code), using
- constructionÂ X applied to AG(F,140P) âŠ‚ AG(F,142P) [i] based on
  1. linear OA(16¹²³, 224, F₁₆, 83) (dual of [224, 101, 84]-code), using algebraic-geometric code AG(F,140P) [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OA(16¹²¹, 224, F₁₆, 81) (dual of [224, 103, 82]-code), using algebraic-geometric code AG(F,142P) [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225 (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.