MinT - Information on Result #858738

Information on Result #858738

Linear OOA(16⁶⁹, 46, F₁₆, 2, 48) (dual of [(46, 2), 23, 49]-NRT-code), using OOA 2-folding based on linear OA(16⁶⁹, 92, F₁₆, 48) (dual of [92, 23, 49]-code), using

discarding factors / shortening the dual code based on linear OA(16⁶⁹, 93, F₁₆, 48) (dual of [93, 24, 49]-code), using
- constructionÂ X applied to AG(F,15P) âŠ‚ AG(F,29P) [i] based on
  1. linear OA(16⁵⁴, 64, F₁₆, 48) (dual of [64, 10, 49]-code), using algebraic-geometric code AG(F,15P) [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(16⁴⁰, 64, F₁₆, 34) (dual of [64, 24, 35]-code), using algebraic-geometric code AG(F,29P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16¹⁵, 29, F₁₆, 13) (dual of [29, 14, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(16¹⁵, 33, F₁₆, 13) (dual of [33, 18, 14]-code), using
      - extended algebraic-geometric code AG_e(F,19P) [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
        a function field by SÃ©mirat [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.