MinT - Information on Result #938555

Information on Result #938555

Linear OOA(3¹⁶⁴, 172, F₃, 2, 52) (dual of [(172, 2), 180, 53]-NRT-code), using trace code based on linear OOA(9⁸², 86, F₉, 2, 52) (dual of [(86, 2), 90, 53]-NRT-code), using

constructionÂ X applied to AG(2;F,93P) âŠ‚ AG(2;F,106P) [i] based on
1. linear OOA(9⁶⁹, 73, F₉, 2, 52) (dual of [(73, 2), 77, 53]-NRT-code), using algebraic-geometric NRT-code AG(2;F,93P) [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(9⁵⁶, 73, F₉, 2, 39) (dual of [(73, 2), 90, 40]-NRT-code), using algebraic-geometric NRT-code AG(2;F,106P) [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74 (see above)
3. linear OOA(9¹³, 13, F₉, 2, 12) (dual of [(13, 2), 13, 13]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9¹³, 16, F₉, 2, 12) (dual of [(16, 2), 19, 13]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,19P) [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(3¹⁶⁵, 172, F₃, 2, 52) (dual of [(172, 2), 179, 53]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(3¹⁶⁴, 86, F₃, 4, 52) (dual of [(86, 4), 180, 53]-NRT-code)	[i]		OOA Folding