MinT - Information on Result #2682850

Information on Result #2682850

Linear OOA(3²⁴⁹, 179, F₃, 3, 83) (dual of [(179, 3), 288, 84]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3²⁴⁶, 178, F₃, 3, 83) (dual of [(178, 3), 288, 84]-NRT-code), using

trace code [i] based on linear OOA(9¹²³, 89, F₉, 3, 83) (dual of [(89, 3), 144, 84]-NRT-code), using
- constructionÂ X applied to AG(3;F,147P) âŠ‚ AG(3;F,165P) [i] based on
  1. linear OOA(9¹⁰⁵, 77, F₉, 3, 83) (dual of [(77, 3), 126, 84]-NRT-code), using algebraic-geometric NRT-code AG(3;F,147P) [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]
  2. linear OOA(9⁸⁷, 77, F₉, 3, 65) (dual of [(77, 3), 144, 66]-NRT-code), using algebraic-geometric NRT-code AG(3;F,165P) [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78 (see above)
  3. linear OOA(9¹⁸, 12, F₉, 3, 17) (dual of [(12, 3), 18, 18]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9¹⁸, 16, F₉, 3, 17) (dual of [(16, 3), 30, 18]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,30P) [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, 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.