MinT - Information on Result #2647414

Information on Result #2647414

Linear OOA(9¹¹⁶, 94, F₉, 3, 67) (dual of [(94, 3), 166, 68]-NRT-code), using strength reduction based on linear OOA(9¹¹⁶, 94, F₉, 3, 68) (dual of [(94, 3), 166, 69]-NRT-code), using

constructionÂ X applied to AG(3;F,162P) âŠ‚ AG(3;F,187P) [i] based on
1. linear OOA(9⁹⁰, 77, F₉, 3, 68) (dual of [(77, 3), 141, 69]-NRT-code), using algebraic-geometric NRT-code AG(3;F,162P) [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(9⁶⁵, 77, F₉, 3, 43) (dual of [(77, 3), 166, 44]-NRT-code), using algebraic-geometric NRT-code AG(3;F,187P) [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78 (see above)
3. linear OOA(9²⁶, 17, F₉, 3, 24) (dual of [(17, 3), 25, 25]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9²⁶, 20, F₉, 3, 24) (dual of [(20, 3), 34, 25]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,35P) [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, 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.