MinT - Information on Result #938606

Information on Result #938606

Linear OOA(3¹⁷², 170, F₃, 2, 57) (dual of [(170, 2), 168, 58]-NRT-code), using trace code based on linear OOA(9⁸⁶, 85, F₉, 2, 57) (dual of [(85, 2), 84, 58]-NRT-code), using

constructionÂ X applied to AG(2;F,88P) âŠ‚ AG(2;F,100P) [i] based on
1. linear OOA(9⁷⁴, 73, F₉, 2, 57) (dual of [(73, 2), 72, 58]-NRT-code), using algebraic-geometric NRT-code AG(2;F,88P) [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(9⁶², 73, F₉, 2, 45) (dual of [(73, 2), 84, 46]-NRT-code), using algebraic-geometric NRT-code AG(2;F,100P) [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74 (see above)
3. linear OOA(9¹², 12, F₉, 2, 11) (dual of [(12, 2), 12, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9¹², 16, F₉, 2, 11) (dual of [(16, 2), 20, 12]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,20P) [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, 170, F₃, 2, 57) (dual of [(170, 2), 167, 58]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3¹⁷², 85, F₃, 4, 57) (dual of [(85, 4), 168, 58]-NRT-code)	[i]		OOA Folding