MinT - Information on Result #858959

Information on Result #858959

Linear OOA(16⁸¹, 53, F₁₆, 2, 52) (dual of [(53, 2), 25, 53]-NRT-code), using OOA 2-folding based on linear OA(16⁸¹, 106, F₁₆, 52) (dual of [106, 25, 53]-code), using

discarding factors / shortening the dual code based on linear OA(16⁸¹, 107, F₁₆, 52) (dual of [107, 26, 53]-code), using
- constructionÂ X applied to AG(F,11P) âŠ‚ AG(F,31P) [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(16³⁸, 64, F₁₆, 32) (dual of [64, 26, 33]-code), using algebraic-geometric code AG(F,31P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16²³, 43, F₁₆, 19) (dual of [43, 20, 20]-code), using
    - discarding factors / shortening the dual code based on linear OA(16²³, 45, F₁₆, 19) (dual of [45, 22, 20]-code), using
      - extended algebraic-geometric code AG_e(F,25P) [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.