MinT - Information on Result #2682135

Information on Result #2682135

Linear OOA(3²²¹, 176, F₃, 3, 71) (dual of [(176, 3), 307, 72]-NRT-code), using 3¹ times duplication based on linear OOA(3²²⁰, 176, F₃, 3, 71) (dual of [(176, 3), 308, 72]-NRT-code), using

trace code [i] based on linear OOA(9¹¹⁰, 88, F₉, 3, 71) (dual of [(88, 3), 154, 72]-NRT-code), using
- constructionÂ X applied to AG(3;F,159P) âŠ‚ AG(3;F,176P) [i] based on
  1. linear OOA(9⁹³, 77, F₉, 3, 71) (dual of [(77, 3), 138, 72]-NRT-code), using algebraic-geometric NRT-code AG(3;F,159P) [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(9⁷⁶, 77, F₉, 3, 54) (dual of [(77, 3), 155, 55]-NRT-code), using algebraic-geometric NRT-code AG(3;F,176P) [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78 (see above)
  3. linear OOA(9¹⁷, 11, F₉, 3, 16) (dual of [(11, 3), 16, 17]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9¹⁷, 16, F₉, 3, 16) (dual of [(16, 3), 31, 17]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,31P) [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.