MinT - Information on Result #858688

Information on Result #858688

Linear OOA(16⁷⁷, 54, F₁₆, 2, 47) (dual of [(54, 2), 31, 48]-NRT-code), using OOA 2-folding based on linear OA(16⁷⁷, 108, F₁₆, 47) (dual of [108, 31, 48]-code), using

discarding factors / shortening the dual code based on linear OA(16⁷⁷, 109, F₁₆, 47) (dual of [109, 32, 48]-code), using
- constructionÂ X applied to AG(F,16P) âŠ‚ AG(F,37P) [i] based on
  1. linear OA(16⁵³, 64, F₁₆, 47) (dual of [64, 11, 48]-code), using algebraic-geometric code AG(F,16P) [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(16³², 64, F₁₆, 26) (dual of [64, 32, 27]-code), using algebraic-geometric code AG(F,37P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16²⁴, 45, F₁₆, 20) (dual of [45, 21, 21]-code), using
    - extended algebraic-geometric code AG_e(F,24P) [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [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.