MinT - Information on Result #1048213

Information on Result #1048213

Linear OOA(3²¹⁸, 168, F₃, 3, 77) (dual of [(168, 3), 286, 78]-NRT-code), using trace code based on linear OOA(9¹⁰⁹, 84, F₉, 3, 77) (dual of [(84, 3), 143, 78]-NRT-code), using

constructionÂ X applied to AG(3;F,153P) âŠ‚ AG(3;F,164P) [i] based on
1. linear OOA(9⁹⁹, 77, F₉, 3, 77) (dual of [(77, 3), 132, 78]-NRT-code), using algebraic-geometric NRT-code AG(3;F,153P) [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(9⁸⁸, 77, F₉, 3, 66) (dual of [(77, 3), 143, 67]-NRT-code), using algebraic-geometric NRT-code AG(3;F,164P) [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78 (see above)
3. linear OOA(9¹⁰, 7, F₉, 3, 10) (dual of [(7, 3), 11, 11]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9¹⁰, 9, F₉, 3, 10) (dual of [(9, 3), 17, 11]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;17,9) [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(3²¹⁸, 168, F₃, 3, 76) (dual of [(168, 3), 286, 77]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3²²¹, 169, F₃, 3, 77) (dual of [(169, 3), 286, 78]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(3²¹⁹, 168, F₃, 3, 77) (dual of [(168, 3), 285, 78]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(3²¹⁸, 84, F₃, 5, 77) (dual of [(84, 5), 202, 78]-NRT-code)	[i]	OOA Folding