MinT - Information on Result #627837

Information on Result #627837

Linear OA(4¹³⁰, 164, F₄, 47) (dual of [164, 34, 48]-code), using trace code based on linear OA(16⁶⁵, 82, F₁₆, 47) (dual of [82, 17, 48]-code), using

discarding factors / shortening the dual code based on linear OA(16⁶⁵, 88, F₁₆, 47) (dual of [88, 23, 48]-code), using
- constructionÂ X applied to AG(F,16P) âŠ‚ AG(F,28P) [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(16⁴¹, 64, F₁₆, 35) (dual of [64, 23, 36]-code), using algebraic-geometric code AG(F,28P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OA(16¹², 24, F₁₆, 11) (dual of [24, 12, 12]-code), using
    - extended algebraic-geometric code AG_e(F,12P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, 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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

None.