MinT - Information on Result #938604

Information on Result #938604

Linear OOA(3¹⁷², 174, F₃, 2, 55) (dual of [(174, 2), 176, 56]-NRT-code), using trace code based on linear OOA(9⁸⁶, 87, F₉, 2, 55) (dual of [(87, 2), 88, 56]-NRT-code), using

constructionÂ X applied to AG(2;F,90P) âŠ‚ AG(2;F,104P) [i] based on
1. linear OOA(9⁷², 73, F₉, 2, 55) (dual of [(73, 2), 74, 56]-NRT-code), using algebraic-geometric NRT-code AG(2;F,90P) [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
  - a function field by GarcÃa and Quoos [i]
2. linear OOA(9⁵⁸, 73, F₉, 2, 41) (dual of [(73, 2), 88, 42]-NRT-code), using algebraic-geometric NRT-code AG(2;F,104P) [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74 (see above)
3. linear OOA(9¹⁴, 14, F₉, 2, 13) (dual of [(14, 2), 14, 14]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9¹⁴, 16, F₉, 2, 13) (dual of [(16, 2), 18, 14]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,18P) [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(3¹⁷³, 174, F₃, 2, 55) (dual of [(174, 2), 175, 56]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3¹⁷², 87, F₃, 4, 55) (dual of [(87, 4), 176, 56]-NRT-code)	[i]		OOA Folding