MinT - Information on Result #1048234

Information on Result #1048234

Linear OOA(3²²², 170, F₃, 3, 77) (dual of [(170, 3), 288, 78]-NRT-code), using trace code based on linear OOA(9¹¹¹, 85, F₉, 3, 77) (dual of [(85, 3), 144, 78]-NRT-code), using

constructionÂ X applied to AG(3;F,153P) âŠ‚ AG(3;F,166P) [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(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 (see above)
3. linear OOA(9¹², 8, F₉, 3, 12) (dual of [(8, 3), 12, 13]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9¹², 9, F₉, 3, 12) (dual of [(9, 3), 15, 13]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;15,9) [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		This result only	Method
1	Linear OOA(3²²³, 170, F₃, 3, 77) (dual of [(170, 3), 287, 78]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3²²², 85, F₃, 5, 77) (dual of [(85, 5), 203, 78]-NRT-code)	[i]		OOA Folding