MinT - Information on Result #1048350

Information on Result #1048350

Linear OOA(3²⁴², 180, F₃, 3, 79) (dual of [(180, 3), 298, 80]-NRT-code), using trace code based on linear OOA(9¹²¹, 90, F₉, 3, 79) (dual of [(90, 3), 149, 80]-NRT-code), using

constructionÂ X applied to AG(3;F,151P) âŠ‚ AG(3;F,171P) [i] based on
1. linear OOA(9¹⁰¹, 77, F₉, 3, 79) (dual of [(77, 3), 130, 80]-NRT-code), using algebraic-geometric NRT-code AG(3;F,151P) [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(9⁸¹, 77, F₉, 3, 59) (dual of [(77, 3), 150, 60]-NRT-code), using algebraic-geometric NRT-code AG(3;F,171P) [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78 (see above)
3. linear OOA(9²⁰, 13, F₉, 3, 19) (dual of [(13, 3), 19, 20]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9²⁰, 16, F₉, 3, 19) (dual of [(16, 3), 28, 20]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,28P) [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3²⁴³, 180, F₃, 3, 79) (dual of [(180, 3), 297, 80]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²⁴², 90, F₃, 5, 79) (dual of [(90, 5), 208, 80]-NRT-code)	[i]		OOA Folding