MinT - Information on Result #1047727

Information on Result #1047727

Linear OOA(2¹¹⁸, 70, F₂, 3, 40) (dual of [(70, 3), 92, 41]-NRT-code), using trace code based on linear OOA(4⁵⁹, 35, F₄, 3, 40) (dual of [(35, 3), 46, 41]-NRT-code), using

constructionÂ X applied to AG(3;F,55P) âŠ‚ AG(3;F,60P) [i] based on
1. linear OOA(4⁵⁵, 32, F₄, 3, 40) (dual of [(32, 3), 41, 41]-NRT-code), using algebraic-geometric NRT-code AG(3;F,55P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
  - an explicitly constructive algebraic function field [i]
2. linear OOA(4⁵⁰, 32, F₄, 3, 35) (dual of [(32, 3), 46, 36]-NRT-code), using algebraic-geometric NRT-code AG(3;F,60P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33 (see above)
3. linear OOA(4⁴, 3, F₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4⁴, 4, F₄, 3, 4) (dual of [(4, 3), 8, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;8,4) [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(2¹¹⁸, 70, F₂, 3, 39) (dual of [(70, 3), 92, 40]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹²¹, 71, F₂, 3, 40) (dual of [(71, 3), 92, 41]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(2¹¹⁹, 70, F₂, 3, 40) (dual of [(70, 3), 91, 41]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2¹¹⁸, 35, F₂, 5, 40) (dual of [(35, 5), 57, 41]-NRT-code)	[i]	OOA Folding
5	Linear OOA(2¹¹⁸, 35, F₂, 6, 40) (dual of [(35, 6), 92, 41]-NRT-code)	[i]	OOA Folding