MinT - Information on Result #1048012

Information on Result #1048012

Linear OOA(3¹⁶⁶, 160, F₃, 3, 57) (dual of [(160, 3), 314, 58]-NRT-code), using trace code based on linear OOA(9⁸³, 80, F₉, 3, 57) (dual of [(80, 3), 157, 58]-NRT-code), using

constructionÂ X applied to AG(3;F,173P) âŠ‚ AG(3;F,178P) [i] based on
1. linear OOA(9⁷⁹, 77, F₉, 3, 57) (dual of [(77, 3), 152, 58]-NRT-code), using algebraic-geometric NRT-code AG(3;F,173P) [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(9⁷⁴, 77, F₉, 3, 52) (dual of [(77, 3), 157, 53]-NRT-code), using algebraic-geometric NRT-code AG(3;F,178P) [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78 (see above)
3. linear OOA(9⁴, 3, F₉, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9⁴, 9, F₉, 3, 4) (dual of [(9, 3), 23, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;23,9) [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		Method
1	Linear OOA(3¹⁶⁶, 160, F₃, 3, 56) (dual of [(160, 3), 314, 57]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3¹⁶⁹, 161, F₃, 3, 57) (dual of [(161, 3), 314, 58]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(3¹⁶⁷, 160, F₃, 3, 57) (dual of [(160, 3), 313, 58]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(3¹⁶⁶, 80, F₃, 5, 57) (dual of [(80, 5), 234, 58]-NRT-code)	[i]	OOA Folding