MinT - Information on Result #938523

Information on Result #938523

Linear OOA(3¹⁵⁸, 168, F₃, 2, 51) (dual of [(168, 2), 178, 52]-NRT-code), using trace code based on linear OOA(9⁷⁹, 84, F₉, 2, 51) (dual of [(84, 2), 89, 52]-NRT-code), using

constructionÂ X applied to AG(2;F,94P) âŠ‚ AG(2;F,105P) [i] based on
1. linear OOA(9⁶⁸, 73, F₉, 2, 51) (dual of [(73, 2), 78, 52]-NRT-code), using algebraic-geometric NRT-code AG(2;F,94P) [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(9⁵⁷, 73, F₉, 2, 40) (dual of [(73, 2), 89, 41]-NRT-code), using algebraic-geometric NRT-code AG(2;F,105P) [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74 (see above)
3. linear OOA(9¹¹, 11, F₉, 2, 10) (dual of [(11, 2), 11, 11]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9¹¹, 16, F₉, 2, 10) (dual of [(16, 2), 21, 11]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,21P) [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(3¹⁵⁹, 168, F₃, 2, 51) (dual of [(168, 2), 177, 52]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3¹⁵⁸, 84, F₃, 4, 51) (dual of [(84, 4), 178, 52]-NRT-code)	[i]		OOA Folding