MinT - Information on Result #2647224

Information on Result #2647224

Linear OOA(9¹⁰⁷, 91, F₉, 3, 63) (dual of [(91, 3), 166, 64]-NRT-code), using strength reduction based on linear OOA(9¹⁰⁷, 91, F₉, 3, 64) (dual of [(91, 3), 166, 65]-NRT-code), using

constructionÂ X applied to AG(3;F,166P) âŠ‚ AG(3;F,187P) [i] based on
1. linear OOA(9⁸⁶, 77, F₉, 3, 64) (dual of [(77, 3), 145, 65]-NRT-code), using algebraic-geometric NRT-code AG(3;F,166P) [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(9²¹, 14, F₉, 3, 20) (dual of [(14, 3), 21, 21]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9²¹, 16, F₉, 3, 20) (dual of [(16, 3), 27, 21]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,27P) [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.