MinT - Information on Result #1048045

Information on Result #1048045

Linear OOA(3¹⁷⁸, 164, F₃, 3, 60) (dual of [(164, 3), 314, 61]-NRT-code), using trace code based on linear OOA(9⁸⁹, 82, F₉, 3, 60) (dual of [(82, 3), 157, 61]-NRT-code), using

constructionÂ X applied to AG(3;F,170P) âŠ‚ AG(3;F,178P) [i] based on
1. linear OOA(9⁸², 77, F₉, 3, 60) (dual of [(77, 3), 149, 61]-NRT-code), using algebraic-geometric NRT-code AG(3;F,170P) [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(9⁷, 5, F₉, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9⁷, 9, F₉, 3, 7) (dual of [(9, 3), 20, 8]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;20,9) [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(3¹⁷⁸, 164, F₃, 3, 59) (dual of [(164, 3), 314, 60]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3¹⁸¹, 165, F₃, 3, 60) (dual of [(165, 3), 314, 61]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(3¹⁷⁹, 164, F₃, 3, 60) (dual of [(164, 3), 313, 61]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(3¹⁷⁸, 82, F₃, 5, 60) (dual of [(82, 5), 232, 61]-NRT-code)	[i]	OOA Folding