MinT - Information on Result #859213

Information on Result #859213

Linear OOA(16⁸¹, 50, F₁₆, 2, 57) (dual of [(50, 2), 19, 58]-NRT-code), using OOA 2-folding based on linear OA(16⁸¹, 100, F₁₆, 57) (dual of [100, 19, 58]-code), using

1 times truncation [i] based on linear OA(16⁸², 101, F₁₆, 58) (dual of [101, 19, 59]-code), using
- constructionÂ X applied to AG(F,5P) âŠ‚ AG(F,24P) [i] based on
  1. linear OA(16⁶¹, 64, F₁₆, 58) (dual of [64, 3, 59]-code), using algebraic-geometric code AG(F,5P) with known gap numbers [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(16⁴⁵, 64, F₁₆, 39) (dual of [64, 19, 40]-code), using algebraic-geometric code AG(F,24P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16²¹, 37, F₁₆, 18) (dual of [37, 16, 19]-code), using
    - discarding factors / shortening the dual code based on linear OA(16²¹, 38, F₁₆, 18) (dual of [38, 17, 19]-code), using
      - extended algebraic-geometric code AG_e(F,19P) [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, 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.