MinT - Information on Result #1048349

Information on Result #1048349

Linear OOA(3²⁴², 182, F₃, 3, 78) (dual of [(182, 3), 304, 79]-NRT-code), using trace code based on linear OOA(9¹²¹, 91, F₉, 3, 78) (dual of [(91, 3), 152, 79]-NRT-code), using

constructionÂ X applied to AG(3;F,152P) âŠ‚ AG(3;F,173P) [i] based on
1. linear OOA(9¹⁰⁰, 77, F₉, 3, 78) (dual of [(77, 3), 131, 79]-NRT-code), using algebraic-geometric NRT-code AG(3;F,152P) [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(9⁷⁹, 77, F₉, 3, 57) (dual of [(77, 3), 152, 58]-NRT-code), using algebraic-geometric NRT-code AG(3;F,173P) [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

The following results depend on this result:

	Result		Method
1	Linear OOA(3²⁴², 182, F₃, 3, 77) (dual of [(182, 3), 304, 78]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3²⁴⁵, 183, F₃, 3, 78) (dual of [(183, 3), 304, 79]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(3²⁴³, 182, F₃, 3, 78) (dual of [(182, 3), 303, 79]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(3²⁴², 91, F₃, 5, 78) (dual of [(91, 5), 213, 79]-NRT-code)	[i]	OOA Folding